First-order Phase Transition Research Articles

Structural stability and adsorption behaviour of CO2-loaded pure silica CHA and ITW zeolites upon compression

The present study investigates the structural stability and adsorption behavior of ultrahigh CO2-loaded pure-silica zeolites chabazite (CHA) and ITQ-12 (ITW) under high pressure conditions. To analyze these properties, we have utilized in situ synchrotron-based X-ray powder diffraction techniques. Lattice indexation provides information of the filling process and, through Rietveld refinements and Fourier recycling methods, we have been able to (i) determine the location and amount of guest carbon dioxide molecules within the cavities of pure-SiO2 CHA zeolite and (ii) tentatively determine that within the channels of the porous pure-SiO2 ITW framework. The filling of the zeolite pores with CO2 molecules was found to have a positive impact on the structural stability of both CHA and ITW under compression, which do not undergo pressure-induced amorphization up to 12.2 GPa and 15.9 GPa, respectively. Interestingly, low compressibility takes place in CHA zeolite below 4 GPa during CO2 loading and a second-order phase transition occurs in CO2-filled ITW zeolite at 2.1 GPa. These results highlight the influence of CO2 adsorption on the compressibility behavior of these zeolites. Overall, our study provides detailed insights into the structural behavior of CO2-loaded CHA and ITW under high pressure and allows comparison with other pure silica zeolites described in the literature.

Thermodynamics and dynamics of coupled complex SYK models.

It has been known that the large-q complex SYK model falls under the same universality class as that of van der Waals (mean-field) and saturates the Maldacena-Shenker-Stanford bound, both features shared by various black holes. This makes the SYK model a useful tool in probing the fundamental nature of quantum chaos and holographic duality. This work establishes the robustness of this shared universality class and chaotic properties for SYK-like models by extending to a system of coupled large-q complex SYK models of different orders. We provide a detailed derivation of thermodynamic properties, specifically the critical exponents for an observed phase transition, as well as dynamical properties, in particular the Lyapunov exponent, via the out-of-time correlator calculations. Our analysis reveals that, despite the introduction of an additional scaling parameter through interaction strength ratios, the system undergoes a continuous phase transition at low temperatures, similar to that of the single SYK model. The critical exponents align with the Landau-Ginzburg (mean-field) universality class, shared with van der Waals gases and various AdS black holes. Furthermore, we demonstrate that the coupled SYK system remains maximally chaotic in the large-q limit at low temperatures, adhering to the Maldacena-Shenker-Stanford bound, a feature consistent with the single SYK model. These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems. We provide a detailed outlook for future work by considering the ``very" low-temperature regime, where we discuss relations with the Hawking-Page phase transition observed in the holographic dual black holes. We present preliminary calculations and discuss the possible follow-ups that might be be taken to make the connection robust.

Observation of competing interactions and field-induced ferromagnetism in noncentrosymmetric cubic Nd3Te4 lattice

Unconventional magnetism is key to advancement in a variety of spintronic applications and thus needs to be explored in new materials. Here, we report the in-depth magnetic studies of noncentrosymmetric Nd3Te4 and findings support the existence of Dzyaloshinskii-Moriya interaction in addition to symmetric exchange interaction among the moments. The large magnetic irreversibility with negative magnetization in M(T) data and associated first-order magnetic transition in isothermal magnetization data suggest the competing interactions resulting in multiple magnetic phases. The gradual evolution of magnetic texture has been probed by changes in the magnetization entropy having interesting characteristics like the inverse magnetocaloric effect. Most importantly, we have probed the existing nontrivial magnetic phase under a low applied magnetic field by ac-χ(T, H) and dc magnetization (M − H) data, having the same critical field in both measurements. The existence of multiple magnetic phases which are interconnected through first-order field-induced magnetic phase transitions have been probed at low field. The transition from paramagnetic to field-induced state for larger applied fields follows a second-order.

Influence of electron and hole doping on structural, Magnetic, and magnetocaloric properties of Ba2FeMoO6 double perovskite

The impact of Sm3+ and Ag+ doping at the Ba2+ site on the structural, magnetic, and magnetocaloric properties of Ba2FeMoO6 (BFMO) double perovskite was compared. Samples were synthesized using the sol–gel method. Rietveld refinement patterns of samples Ba2-xAxFeMoO6 (A=Sm, Ag, x = 0.0, 0.025) showed all samples had cubic structures with Fm-3 m space group and no impurity. The lattice parameters and unit cell of the Ba1.975Sm0.025FeMoO6 (BSFMO), and Ba1.975Ag0.025FeMoO6 (BAFMO) samples decreased compared to the parent sample. X-ray photoelectron spectroscopy confirmed that Fe and Mo ions were mixed valence for all samples. The results of magnetization versus temperature (M−T) showed an increase for BSFMO and a decrease for BAFMO samples under an external magnetic field of 0.05 T. The magnetic study indicated a decrease in the transition temperature for BSFMO (∼303 K) and an increase for BAFMO (∼321 K) to compare with the parent sample (∼310 K). The maximum value of magnetic entropy changes (ΔSMmax)of the BFMO, BSFMO, and BAFMO samples at H=3 T obtained 0.92 Jkg-1K−1, 0.75 Jkg-1K−1, and 0.39 Jkg-1K−1, respectively, and the second-order magnetic phase occurred around the transition temperature. For BFMO, BSFMO, and BAFMO, the relative cooling power (RCP) is 34.48 J/kg, 32.25 J/kg, and 21.97 J/kg, respectively. The second-order magnetic phase transition occurred around the transition temperature for all samples using the energy criterion as well as the universal curve method. In addition, we used Widom’s law to determine the critical exponent of the samples, which provides a new thermodynamic method to determine the magnetic phase transition. The results of the magnetocaloric effect indicate that although the maximum entropy changes and relative cooling decrease with doping Ag and Sm ions, they have a wide temperature range of magnetic entropy changes compared to the pristine sample, which can be candidates for magnetic cooling.

Quantitative Disorder Effects in Low-Dimensional Spin Systems

The Imry–Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin systems are ‘rounded’ by the addition of a quenched random field coupled to the quantity undergoing the transition. The phenomenon applies to a wide class of spin systems in dimensions d≤2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 2$$\\end{document} and to spin systems possessing a continuous symmetry in dimensions d≤4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 4$$\\end{document}. This work provides quantitative estimates for the Imry–Ma phenomenon: in a cubic domain of side length L, we study the effect of the boundary conditions on the spatial and thermal average of the quantity coupled to the random field. We show that the boundary effect diminishes at least as fast as an inverse power of loglogL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log \\log L$$\\end{document} in general two-dimensional spin systems. For systems possessing a continuous symmetry, we show that the boundary effect diminishes at least as fast as an inverse power of L in two and three dimensions and at least as fast as an inverse power of loglogL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log \\log L$$\\end{document} in four dimensions. Finally, we establish a partial uniqueness results for translation-covariant Gibbs states, and prove that, for almost every realization of the random field, all such states must agree on the thermally-averaged value of the quantity coupled to the random field. Specific models of interest for the obtained results include the random-field q-state Potts model, the Edwards-Anderson spin glass model, and the random-field spin O(n) models.

First-order electroweak phase transition at finite density

We study the Electroweak phase transition with the Standard Model effective field theory at finite temperature and finite density. Utilizing the dimensional reduction approach, we construct the tree dimensional thermal effective field theory at finite density and investigate the phase transition dynamics. We evaluate how the results depend on the renormalization scale and the chemical potential. Our results show that, with the tree dimensional thermal effective potential at 2-loop level, we can effectively reduce the theoretical uncertainty in the calculations of the phase transition parameters due to the renormalization scale dependence, and the new physics scale is restricted to be Λ ≲ (770 − 800) GeV by the baryon number washout avoidance condition. Meanwhile, the presence of the chemical potential would affect the phase transition parameter and make the constraints from the baryon number washout avoidance condition more strict, especially for weaker first-order phase transition scenarios at higher new physics scales.

Technology and Dielectric Properties of BLT4 Ceramics Modified with Special Glass

Lead-boron special glass was doped into Ba0.996La0.004Ti0.999O3 (BLT4) ceramics in order to control the sintering process and grain growth, consequently obtaining materials with a well-developed microstructure. Changes in the microstructure resulted in a significant decrease in electrical permittivity along with a substantial increase in its frequency dispersion. Glass-doped ceramics, similar to pure BLT4, are characterized by a first-order phase transition from the ferroelectric phase to the paraelectric phase. The temperature of this transition shifts slightly towards higher values with the increase in glass dopant concentration.

Quantum phase transitions and cat states in cavity-coupled quantum dots

We study double quantum dots coupled to a quasistatic cavity mode with high mode-volume compression allowing for strong light-matter coupling. Besides the cavity-mediated interaction, electrons in different double quantum dots interact with each other via dipole-dipole (Coulomb) interaction. There is a first-order cavity-induced ferroelectric quantum phase transition when the attractive dipolar interaction is smaller than the critical value defined by the energy splitting in DQDs and a smooth transition, otherwise. We show that, in the smooth transition region, both the ground and the first excited states of an array of double quantum dots are cat states. Such states are actively discussed as high-fidelity qubits for quantum computing, and thus our proposal provides a platform for semiconductor implementation of such qubits. We also calculate gauge-invariant observables such as the net dipole moment, the optical conductivity, and the absorption spectrum beyond the semiclassical approximation. The results are robust against cavity losses and variations of system parameters. Published by the American Physical Society 2024

Continuous reduction and phase transformation mechanism of pellets in lumpy zone based on dissected hydrogen blast furnace

The continuous phase transition phenomena and mechanism of pellets in the hydrogen blast furnace is achieved by dissecting the 40m3 hydrogen blast furnace. The results of the dissection reveal that the lumpy zone extends to the bosh of the hydrogen blast furnace (HBF), while it ends at about 2/3 of the stack in traditional blast furnace. The iron oxide (FeOx) began to appear in the upper stack, while the iron started to appear in the lower stack. The reduction rate and metallization rate at the bosh are measured at 95.18% and 95.54%. The content of ferrous oxide (FeO) decreases significantly (measured at 1.73% at the bosh), resulting in an increase in the melting point of the primary slag and a deterioration of its fluidity. FeOx formed in the upper stack continuously diffuses and merges into the gangue, which affects the subsequent transformation of FeOx. FeOx shows a preference for interacting with SiO2, CaO, and MgO, directly influencing the formation of slag in the cohesive zone. These findings offer valuable insights for numerical simulation and research on hydrogen-rich operation.

Relativistic hydrodynamics with phase transition

Assessing the applicability of hydrodynamic expansions close to phase transition points is crucial from either theoretical or phenomenological points of view. We explore this within the gauge/gravity duality, using the Einstein–Klein–Gordon model, a bottom-up string theory construction. This model incorporates a parameter, B4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_4$$\\end{document}, that simulates different types of phase transitions in the strongly coupled field theory existing at the boundary. We thoroughly examine the thermodynamics and dynamics of time-dependent, linearized perturbations in the spin-2, spin-1, and spin-0 sectors. Our findings suggest that ‘hydrodynamic series breakdown near transition points” is valid exclusively for second-order phase transitions, not for crossovers or first-order phase transitions. Additionally, we observe that the high-temperature and low-temperature limits of the radius of convergence for the hydrodynamic series (qc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q^2_c$$\\end{document}) are equal. We also discover that the relationship (Max|qc2|)spin-2<(Max|qc2|)spin-0<(Max|qc2|)spin-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\ ext {Max}|q^2_c|)_{\ ext {spin-2}}< (\ ext {Max}|q^2_c|)_{\ ext {spin-0}} < (\ ext {Max}|q^2_c|)_{\ ext {spin-1}}$$\\end{document} is consistent for different spin sectors, regardless of the phase transition type. At the chaos point, we observe the emergence of pole-skipping behavior for both gravity and scalar perturbations at ωn=-2πTni\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _n = -2\\pi T n i$$\\end{document}. Lastly, comparing the chaos momentum with qc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q^2_c$$\\end{document}, we find that qps2<qc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q^2_{ps} < q^2_c$$\\end{document}, except for extremely high temperatures.

Self-organized time crystal in driven-dissipative quantum system

Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time-translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field theories, which fail to address the problem of whether the continuous time-translation symmetry can be broken in noisy, spatially extended systems absent in all-to-all couplings. Here, we propose a CTC realized in a quantum contact model through self-organized bistability. The CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of many-body synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time linearly diverging with system size, thus also constituting a boundary time crystal. Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems. Published by the American Physical Society 2024

Real-Space Imaging of Intrinsic Symmetry-Breaking Spin Textures in a Kagome Lattice.

The electronic orders in kagome materials have emerged as a fertile platform for studying exotic quantum states, and their intertwining with the unique kagome lattice geometry remains elusive. While various unconventional charge orders with broken symmetry is observed, the influence of kagome symmetry on magnetic order has so far not been directly observed. Here, using a high-resolution magnetic force microscopy, it is, for the first time, observed a new lattice form of noncollinear spin textures in the kagome ferromagnet in zero magnetic field. Under the influence of the sixfold rotational symmetry of the kagome lattice, the spin textures are hexagonal in shape and can further form a honeycomb lattice structure. Subsequent thermal cycling measurements reveal that these spin textures transform into a non-uniform in-plane ferromagnetic ground state at low temperatures and can fully rebuild at elevated temperatures, showing a strong second-order phase transition feature. Moreover, some out-of-plane magnetic moments persist at low temperatures, supporting the Kane-Mele scenario in explaining the emergence of the Dirac gap. The observations establish that the electronic properties, including both charge and spin orders, are strongly coupled with the kagome lattices.

Free Energy Evaluation of Cavity Formation in Metastable Liquid Based on Stochastic Thermodynamics.

Nucleation is a fundamental and general process at the initial stage of first-order phase transition. Although various models based on the classical nucleation theory (CNT) have been proposed to explain the energetics and kinetics of nucleation, detailed understanding at nanoscale is still required. Here, in view of the homogeneous bubble nucleation, we focus on cavity formation, in which evaluation of the size dependence of free energy change is the key issue. We propose the application of a formula in stochastic thermodynamics, the Jarzynski equality, for data analysis of molecular dynamics (MD) simulation to evaluate the free energy of cavity formation. As a test case, we performed a series of MD simulations with a Lennard-Jones (LJ) fluid system. By applying an external spherical force field to equilibrated LJ liquid, we evaluated the free energy change during cavity growth as the Jarzynski's ensemble average of required works. A fairly smooth free energy curve was obtained as a function of bubble radius in metastable liquid of mildly negative pressure conditions.

Non-linear dynamics and critical phenomena in the holographic landscape of Weyl semimetals

This study presents a detailed analysis of critical phenomena in a holographic Weyl semi-metal (WSM) using the D3/D7 brane configuration. The research explores the non-linear response of the longitudinal current J when subjected to an external electric field E at both zero and finite temperatures. At zero temperature, the study identifies a potential quantum phase transition in the J-E relationship, driven by background parameters the particle mass, and axial gauge potential. This transition is characterized by a unique reconnection phenomenon resulting from the interplay between WSM-like and conventional nonlinear conducting behaviors, indicating a quantum phase transition.Additionally, at non-zero temperatures with dissipation, the system demonstrates first- and second-order phase transitions as the electric field and axial gauge potential are varied. The longitudinal conductivity is used as an order parameter to identify the current-driven phase transition. Numerical analysis reveals critical exponents in this non-equilibrium phase transition that show similarities to mean-field values observed in metallic systems.

The imprint of conservation laws on correlated particle production

The study of event-by-event fluctuations of net-baryon number in a subspace of full phase space is a promising direction for deciphering the structure of strongly interacting matter created in collisions of relativistic heavy nuclei. Such fluctuations are generally suppressed by exact baryon number conservation. Moreover, the suppression is stronger if baryon number is conserved locally. In this report we present a conceptually new approach to quantify correlations in rapidity space between baryon-antibaryon, baryon-baryon, and antibaryon-antibaryon pairs and demonstrate their impact on net-baryon number fluctuations. For the special case of Gaussian rapidity distributions, we use the Cholesky factorization of the covariance matrix, while the general case is introduced by exploiting the well-known Metropolis and Simulated Annealing methods. The approach is based on the use of the canonical ensemble of statistical mechanics for baryon number and can be applied to study correlations between baryons as well as strange and/or charm hadrons. It can also be applied to describe relativistic nuclear collisions leading to the production of multi-particle final states. One application of our method is the search for formation of proton clusters at low collision energies emerging as a harbinger of the anticipated first-order chiral phase transition. In a first step, the results obtained are compared to the recent measurements from the CERN ALICE collaboration. Such investigations are key to explore the phase diagram of strongly interacting matter and baryon production mechanisms at energy scales from several GeV to several TeV.

Phase transitions and thermodynamic cycles in the broken PT-regime

We propose a new type of quantum thermodynamic cycle whose efficiency is greater than the one of the classical Carnot cycle for the same conditions for a system when viewed as homogeneous. In our model, this type of cycle only exists in the low-temperature regime in the spontaneously broken parity-time-reversal (PT) symmetry regime of a non-Hermitian quantum theory and does not manifest in the PT-symmetric regime. We discuss this effect for an ensemble based on a model of a single boson coupled in a non-Hermitian way to a bath of different types of bosons with and without a time-dependent boundary. The cycle cannot be set up when considering our system as heterogeneous, i.e. undergoing a first-order phase transition. Within that interpretation, we find that the entropy is vanishing throughout the spontaneously broken PT-regime.

Triplon analysis of magnetic disorder and order in maple-leaf Heisenberg magnet

The nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice formed by hexagons (couplingJh), triangles (couplingJt), and dimers (couplingJd), is investigated in a parameter regime whereJh>0andJt,Jd<0. This investigation aims to identify regions hosting exotic valence-bond solid states. Two potential magnetically disordered ground states are identified, and their stability is assessed through plaquette-triplon mean-field analyses. The resulting quantum phase diagram reveals that at large|Jt|and|Jd|, the system adopts a magnetically disordered dimerized VBS state, while for small|Jd|, it stabilizes a Néel state. A second-order phase transition from the dimerized phase to a Néel phase is observed, which, being Landau-forbidden, suggests the potential presence of exotic phenomena such as a deconfined quantum critical point or the appearance of a quantum spin liquid. This work provides insights into the phase diagram of the nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice and lays the groundwork for further investigations into its intriguing physics.

Near-room-temperature magnetic properties and magnetocaloric effect of polycrystalline and nano-scale manganites Pr(0.65-x)NdxSr0.35MnO3 (x ≤ 0.35)

Here we report investigations of structural, electrical and magnetic properties of bulk and nano-sized Pr0.65-xNdxSr0.35MnO3 compounds (x ≤ 0.35). Polycrystalline compounds were produced by solid – state reaction and nanocrystalline samples were obtained by sol–gel method. Analysis of x-ray diffraction patterns revealed a change in lattice structure from ‘Pbnm’ to ‘R3c’ symmetry, with diminishing cell volume upon increasing Nd ions substitution for all samples. Optical microscopy was used for bulk surface morphology and transmission electron microscopy was implemented for nano-sized samples. Iodometric titration showed oxygen deficiency for bulk compounds and oxygen excess for nano-sized particles. Measurements of resistivity of bulk samples revealed a single peak at temperatures associated with grain boundary conditions and with ferromagnetic/paramagnetic transition and negative magnetoresistivity. Critical magnetic behavior analysis disclosed that the polycrystalline samples are governed by a tricritical mean field and by 3D Heisenberg models while nanocrystalline samples are governed by a mean field model. Curie temperature Tc values remain in near room temperature range for all bulk compounds; they lower with increasing Nd ions substitution from 295 K for the parent bulk compound to 268 K for x = 0.35. Tc is lowered from 255 K for the parent nano-sized compound in small temperature intervals. All compounds exhibit second-order magnetic phase transitions and relatively high magnetic entropy change, with the highest value of 5.74 J/kgK for x = 0.25 bulk sample in μ˳∆H = 4 T. Strong magnetocaloric effect, stability and the possibility of fine-tuning Tc by Nd ions substitution make the investigated bulk polycrystalline compounds promising for application in magnetic refrigeration. Nano-sized samples possess lower magnetic entropy changes of maximum 2.4 J/kgK in μ˳∆H = 4 T for x = 0.15, but wider effective entropy change temperature (δTfwhm) and relative cooling power on par with other manganites, bringing them into the conversation as a viable option in cooling materials.

Spinodal slowing down and scaling in a holographic model

The dynamics of first-order phase transitions in strongly coupled systems are relevant in a variety of systems, from heavy ion collisions to the early universe. Holographic theories can be used to model these systems, with fluctuations usually suppressed. In this case the system can come close to a spinodal point where theory and experiments indicate that the behaviour should be similar to a critical point of a second-order phase transition. We study this question using a simple holographic model and confirm that there is critical slowing down and scaling behaviour close to the spinodal point, with precise quantitative estimates. In addition, we determine the start of the scaling regime for the breakdown of quasistatic evolution when the temperature of a thermal bath is slowly decreased across the transition. We also extend the analysis to the dynamics of second-order phase transitions and strong crossovers.

A Jacobian-free pseudo-arclength continuation method for phase transitions in inhomogeneous thermodynamic systems.

Developing phase diagrams for inhomogeneous systems in thermodynamics is difficult, in part, due to the large phase space and the possibility of unstable and metastable solutions arising from first-order phase transitions. Pseudo-arclength continuation (PAC) is a method that allows one to trace out stable and unstable solutions of nonlinear systems. Typically, PAC utilizes the Jacobian in order to implement Newton (or quasi-Newton) steps. In this work, we present a Jacobian-free PAC method that is amenable to the usual workflows in inhomogeneous thermodynamics. We demonstrate our method in systems that have first-order phase transitions, including a novel example of polyelectrolyte complex coacervation in confinement, where multiple surface phase transitions occur and can overlap with one another.