First-order Transition Line Research Articles

Multicritical point of the three-dimensional Z2 gauge Higgs model

We investigate the multicritical behavior of the three-dimensional ${\mathbb{Z}}_{2}$ gauge Higgs model at the multicritical point (MCP) of its phase diagram, where one first-order transition line and two continuous Ising-like transition lines meet. The duality properties of the model determine some features of the multicritical behavior at the MCP located along the self-dual line. Moreover, we argue that the system develops a multicritical $XY$ behavior at the MCP, which is controlled by the stable $XY$ fixed point of the three-dimensional multicritical Landau-Ginzburg-Wilson field theory with two competing scalar fields associated with the continuous ${\mathbb{Z}}_{2}$ transition lines meeting at the MCP. This implies an effective enlargement of the symmetry of the multicritical modes at the MCP to the continuous group O(2). We also provide numerical results to support the multicritical $XY$ scenario.

Field-induced multiple quantum phase transitions in the antiferromagnetic Kondo-lattice compound CeRhAl4Si2

We report a comprehensive phase diagram of the antiferromagnetic Kondo-lattice compound ${\mathrm{CeRhAl}}_{4}{\mathrm{Si}}_{2}$ down to 0.3 K by investigating electrical resistivity, magnetoresistivity, and Hall resistivity under the magnetic field along the $c$ axis. At zero field, ${\mathrm{CeRhAl}}_{4}{\mathrm{Si}}_{2}$ undergoes two successive antiferromagnetic transitions at ${T}_{\mathrm{N}1}=14.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}2}=8.4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, respectively. Upon applying magnetic field, the first-order transition of ${T}_{\mathrm{N}2}$ is continuously suppressed at the critical field of 5.5 T. On the other hand, the smooth suppression of the second-order transition of ${T}_{\mathrm{N}1}$ terminates at a tricritical point of 6.6 T and 4.7 K, followed by a first-order transition line and an additional phase transition line, which are monotonically suppressed at 6.7 and 7.2 T, respectively, implying the field-induced multiple quantum phase transitions. Particularly, in the paramagnetic region before the Fermi liquid behavior is fully developed, a quantum critical phase with non-Fermi liquid behavior is revealed, indicating a potential spin liquid state that was predicted from the global quantum phase diagram. These results suggest that ${\mathrm{CeRhAl}}_{4}{\mathrm{Si}}_{2}$ is a promising candidate to study a quantum phase transition that occurs in electronic systems with high degree of frustration.

Strain-tunable metamagnetic critical endpoint in Mott insulating rare-earth titanates

Rare-earth titanates are Mott insulators whose magnetic ground state -- antiferromagnetic (AFM) or ferromagnetic (FM) -- can be tuned by the radius of the rare-earth element. Here, we combine phenomenology and first-principles calculations to shed light on the generic magnetic phase diagram of a chemically substituted titanate on the rare-earth site that interpolates between an AFM and a FM state. Octahedral rotations present in these perovskites cause the AFM order to acquire a small FM component -- and vice-versa -- removing any multicritical point from the phase diagram. However, for a wide parameter range, a first-order metamagnetic transition line terminating at a critical endpoint survives inside the magnetically ordered phase. Like the liquid-gas transition, a Widom line emerges from the endpoint, characterized by enhanced fluctuations. In contrast to metallic FMs, this metamagnetic transition involves two symmetry-equivalent and insulating canted spin states. Moreover, instead of a magnetic field, we show that uniaxial strain can be used to tune this transition to zero temperature, inducing a quantum critical endpoint.

Statistical mechanics of coupled supercooled liquids in finite dimensions

We study the statistical mechanics of supercooled liquids when the system evolves at a temperature TT with a field \epsilonϵ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature T_0T0. We use mean-field theory to fully characterize the influence of the reference temperature T_0T0, and we mainly study the case of a fixed, low-T_0T0 value in computer simulations. We numerically investigate the extended phase diagram in the (\epsilon,T)(ϵ,T) plane of model glass-forming liquids in spatial dimensions d=2d=2 and d=3d=3, relying on umbrella sampling and reweighting techniques. For both 2d2d and 3d3d cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero \epsilonϵ ending in a critical point in the universality class of the random-field Ising model (RFIM) in d=3d=3. In d=2d=2 instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature T_gTg. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between 2d2d and 3d3d glass-formers.

Phase structure of the CP(1) model in the presence of a topological θ -term

We numerically study the phase structure of the $CP(1)$ model in the presence of a topological $\ensuremath{\theta}$-term, a regime afflicted by the sign problem for conventional lattice Monte Carlo simulations. Using a bond-weighted tensor renormalization group method, we compute the free energy for inverse couplings ranging from $0\ensuremath{\le}\ensuremath{\beta}\ensuremath{\le}1.1$ and find a $CP$-violating, first-order phase transition at $\ensuremath{\theta}=\ensuremath{\pi}$. In contrast to previous findings, our numerical results provide no evidence for a critical coupling ${\ensuremath{\beta}}_{c}<1.1$ above which a second-order phase transition emerges at $\ensuremath{\theta}=\ensuremath{\pi}$ and/or the first-order transition line bifurcates at $\ensuremath{\theta}\ensuremath{\ne}\ensuremath{\pi}$. If such a critical coupling exists, as suggested by Haldane's conjecture, our study indicates that is larger than ${\ensuremath{\beta}}_{c}>1.1$.

Decompression dynamics of high density amorphous ice above and below the liquid-liquid critical point

We investigate via numerical simulations of the TIP4P/Ice model the isothermal decompression of high density amorphous ice (HDA) mirroring the experimental protocol followed by recent experiments [H. K. Kim, et al., Science 370 , 978, 2020]. Taking advantage of the recent determination of the TIP4P/Ice liquid-liquid critical point, we decompress our samples at temperatures both below and above the critical temperature. We follow the crossover between high and low density, complementing the time evolution of the structure factor with the time evolution of microscopic descriptors. Our results support the interpretation of the experimental pathway as a structural change from high to low density states through a first-order transition line. In the simulation study we do not observe nucleation events, but rather a spinodal-like non-equilibrium transformation, which offers an explanation on why the decompression process even at sub-critical temperatures may result in a continuous time evolution of the density and of the microscopic descriptors.

Quantum criticality and spin liquid phase in the Shastry-Sutherland model

Using the density-matrix renormalization group method for the ground state and excitations of the Shastry- Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of first-order transitions and a gapless spin liquid phase. The frustrated Shastry-Sutherland model is close to the critical point but slightly inside the spin liquid phase, while previously studied unfrustrated models cross the first-order line. We also argue that recent heat capacity measurements in SrCu2(BO3)2 show evidence of the proposed spin liquid at pressures between 2.6 and 3 GPa.

Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets

The phase diagrams of highly frustrated quantum spin systems can exhibit first-order quantum phase transitions and thermal critical points even in the absence of any long-ranged magnetic order. However, all unbiased numerical techniques for investigating frustrated quantum magnets face significant challenges, and for generic quantum Monte Carlo methods the challenge is the sign problem. Here we report on a general quantum Monte Carlo approach with a loop-update scheme that operates in any basis, and we show that, with an appropriate choice of basis, it allows us to study a frustrated model of coupled spin-1/2 trimers: simulations of the trilayer Heisenberg antiferromagnet in the spin-trimer basis are sign-problem-free when the intertrimer couplings are fully frustrated. This model features a first-order quantum phase transition, from which a line of first-order transitions emerges at finite temperatures and terminates in a thermal critical point. The trimer unit cell hosts an internal degree of freedom that can be controlled to induce an extensive entropy jump at the quantum transition, which alters the shape of the first-order line. We explore the consequences for the thermal properties in the vicinity of the critical point, which include profound changes in the lines of maxima defined by the specific heat. Our findings reveal trimer quantum magnets as fundamental systems capturing in full the complex thermal physics of the strongly frustrated regime.

Probing three-state Potts nematic fluctuations by ultrasound attenuation

Motivated by recent studies of three-state Potts nematic states in magic-angle twisted bilayer graphene and doped-${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, we analyze the impact of critical nematic fluctuations on the low-energy properties of phonons. In this study, we propose how to identify the three-state Potts nematic fluctuations by ultrasound attenuation. The Gaussian fluctuation analysis shows that the Landau damping term becomes isotropic due to fluctuations of the ${C}_{3}$-breaking bond-order, and the nematoelastic coupling is also shown to be isotropic. These two features lead to an isotropic divergence of the transverse sound attenuation coefficient and an isotropic lattice softening, in contrast to the case of the ${C}_{4}$-breaking bond-order, which shows strong anisotropy. Moreover, we use a mean-field approximation and discuss the impurity effects. The transition temperature takes its maximum near the filling of the van Hove singularity, and the large density of states favors the nematic phase transition. It turns out that the phase transition is of weak first-order in the wide range of filling and, upon increasing the impurity scattering, the first-order transition line at low temperatures gradually shifts towards the second-order line, rendering the transition a weak first-order in a wider range of parameters. Furthermore, it is confirmed that the enhancement of the ultrasound attenuation coefficient will be clearly observed in experiments in the case of a weak first-order phase transition.

Electroprewetting near a flat charged surface.

We look at the wetting of a pure fluid in contact with a charged flat surface. In the bulk, the fluid is a classical van der Waals fluid containing dissociated ions. The presence of wall and ions leads to strong dielectrophoretic and electrophoretic forces that increase the fluid's density at the wall. We calculate the fluid's profiles analytically and numerically and obtain the energy integrals. The critical surface potential for prewetting is obtained. In the phase diagrams, the line of first-order transition meets a second-order transition line at a critical point whose temperature can be higher or lower than the bulk critical temperature. The results are relevant to droplet nucleation around charged particles in the atmosphere and could possibly explain deviations from expected nucleation rates.

Liquid nucleation around charged particles in the vapor phase.

We theoretically investigate the nucleation of liquid droplets from vapor in the presence of a charged spherical particle. Due to field gradients, sufficiently close to the critical pointof the vapor-gas system, the charge destabilizes the vapor phase and initiates a phase transition. The fluid's free energy is described by the van der Waals expression augmented by electrostatic energy and a square-gradient term. We calculate the equilibrium density profile at arbitrary temperatures, particle charges, and vapor densities. In contrast to classical nucleation theory, here, both liquid and vapor phases are different from the bulk phases because they are spatially nonuniform. In addition, the theory applies to both sharp and diffuse interfaces and calculates the surface tension self-consistently. We find the composition profiles and integrate them to get the adsorption near the particle. We find that the adsorption changes discontinuously at a first-order phase transition line. This line becomes a second-order phase transition at high enough temperatures. We describe the transition pointnumerically and provide approximate analytical expressions for it. Similarly to prewetting, the adsorption diverges at the binodal phase boundary. We construct a phase diagram indicating changes in the binodal, spinodal, and critical temperature. It is shown that the field gradient enlarges the range of temperature and vapor density where liquid can nucleate.

Thermodynamic theory of PbxSr1-xTiO3 solid solutions

The thermodynamic potential of the PbxSr1-xTiO3 solid solutions has been determined for the entire range of component concentrations. A phase diagram has been constructed, which contains: a critical point at which the line of second-order phase transitions passes into the line of first-order transitions between the cubic and tetragonal phases; a tricritical point at which the cubic, tetragonal, and rhombohedral phases converge; the multicritical point at which at low temperatures six phases converge along the lines of second-order transitions. The obtained T-x phase diagram of PbxSr1-xTiO3 shows the possibility of the existence of ferroelectric phases that were not previously observed in experiments.

Hot and dense quark-gluon plasma thermodynamics from holographic black holes

We present new results on the equation of state and transition line of hot and dense strongly interacting QCD matter, obtained from a bottom-up Einstein-Maxwell-Dilaton holographic model. We considerably expand the previous coverage in baryon densities in this model by implementing new numerical methods to map the holographic black hole solutions onto the QCD phase diagram. We are also able to obtain, for the first time, the first-order phase transition line in a wide region of the phase diagram. Comparisons with the most recent lattice results for the QCD thermodynamics are also presented.

Effects of the random single-ion anisotropy on the spin-1 Blume-Emery-Griffiths model

The Blume-Emery-Griffiths (BEG) model is considered on the Bethe lattice (BL) in terms of exact recursion relations (ERR) under the effect of a crystal field (D) which was either turned on or off randomly for a given probability. The repulsive case of biquadratic exchange interaction ((K < 0)) between the nearest-neighbor (NN) spins is assumed and the effects of changing the coordination number are also investigated. The thermal variation of the order-parameters, i.e. dipole and quadrupole moments, is examined to obtain the phase diagrams. Very rich phase diagrams with the second- and first-order phase transition lines, tricritical, bicritical and critical end points and the occurrence of reentrant behavior are observed. Different phase regions were explored which include the ferromagnetic (F), paramagnetic (P), staggered quadrupolar (SQ) and ferrimagnetic (FI) phases.

Phase transition in the binary mixture of jammed particles with large size dispersity

It has been well established that particulate systems show the jamming transition and critical scaling behaviors associated with it. However, our knowledge is limited to (nearly) monodisperse systems. Recently, a binary mixture of jammed particles with large size dispersity was studied, and it was suggested that two distinct jammed phases appeared. Here, we conduct a thorough numerical study on this system with a special focus on the statistics of and finite-size effects on the fraction of small particles that participate in the rigid network. We present strong evidence that two distinct jammed phases appear depending on the pressure and composition of two species, which are separated by the first-order phase transition. In one of two phases, only large particles are jammed, whereas both small and large particles are jammed in the other phase. We also describe the phase diagram in the pressure-composition plane, where the first-order phase transition line terminates at a critical point. In addition, we investigate the mechanical properties in terms of the elastic moduli over the phase diagram and find that discontinuous changes in elastic moduli emerge across the phase transition. Remarkably, despite the discontinuities, the elastic moduli in each jammed phase exhibit identical scaling laws to those in the monodisperse systems.

A quantum magnetic analogue to the critical point of water.

At the liquid-gas phase transition in water, the density has a discontinuity at atmospheric pressure; however, the line of these first-order transitions defined by increasing the applied pressure terminates at the critical point1, a concept ubiquitous in statistical thermodynamics2. In correlated quantum materials, it was predicted3 and then confirmed experimentally4,5 that a critical point terminates the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge carrier density. In quantum spin systems, continuous quantum phase transitions6 have been controlled by pressure7,8, applied magnetic field9,10 and disorder11, but discontinuous quantum phase transitions have received less attention. The geometrically frustrated quantum antiferromagnet SrCu2(BO3)2 constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model12-14 and displays exotic phenomena including magnetization plateaus15, low-lying bound-state excitations16, anomalous thermodynamics17 and discontinuous quantum phase transitions18,19. Here we control both the pressure and the magnetic field applied to SrCu2(BO3)2 to provide evidence of critical-point physics in a pure spin system. We use high-precision specific-heat measurements to demonstrate that, as in water, the pressure-temperature phase diagram has a first-order transition line that separates phases with different local magnetic energy densities, and that terminates at an Ising critical point. We provide a quantitative explanation of our data using recently developed finite-temperature tensor-network methods17,20-22. These results further our understanding of first-order quantum phase transitions in quantum magnetism, with potential applications in materials where anisotropic spin interactions produce the topological properties23,24 that are useful for spintronic applications.

Phase diagram for strongly interacting matter in the presence of a magnetic field using the Polyakov–Nambu–Jona-Lasinio model with magnetic field dependent coupling strengths

We study the phase diagram for strongly interacting matter using the 't Hooft determinant extended Nambu--Jona-Lasinio model with a Polyakov loop in the light and strange quark sectors (\emph{up}, \emph{down} and \emph{strange}) focusing on the effect of a magnetic field dependence of the coupling strengths of these interactions. This dependence was obtained so as to reproduce recent lattice QCD results for the magnetic field dependence of the quarks dynamical masses. A finite magnetic field is known to induce several additional first-order phase transition lines with the respective Critical End Points (CEP) in the temperature-quark chemical potential phase diagram when compared to the zero magnetic field case. A study of the magnetic field dependence in the range $eB=0-0.6~\mathrm{GeV}^2$ of the location of these CEPs reveals that the initial one as well as several of the new ones only survive up to a critical magnetic field. Only two remain in the upper limit of the studied magnetic field strength. A comparison of the results obtained with versions of the model with and without Polyakov loop is also done. We also found that the inclusion of the magnetic field dependence on the coupling strengths, while not changing the qualitative features of the phase diagram, affects the location of these CEPs. The comparison of results with and without a regularization cutoff in the medium part of the integrals does not show a significant change.

Existence of a quadruple point in a binary ferroelectric phase diagram

In experimentally measured temperature-composition ferroelectric phase diagrams of ${\mathrm{BaTiO}}_{3}$-based binary systems, a quadruple point where cubic (C), tetragonal (T), orthorhombic (O), and rhombohedral (R) phases converge has been frequently reported in previous work. More interestingly, the quadruple points are experimentally found to behave as a critical point with large enhancement in properties. However, it has remained a fundamental question as to whether a quadruple point in a binary ferroelectric system defies the thermodynamic phase rule and whether such a point necessarily goes critical. In this study, it is demonstrated by Landau theory that a C-T-O-R quadruple point in a binary ferroelectric system can only exist in the form of a unique type of critical point at which two first-order transition lines and two second-order ones meet, and such critical quadruple points do not defy the thermodynamic phase rule. It is further shown that at such a critical C-T-O-R quadruple point, the system exhibits infinitely large piezoelectric coefficients, which agrees with the high piezoelectricity observed at the C-T-O-R quadruple point in a number of ${\mathrm{BaTiO}}_{3}$-based binary ferroelectric systems and also helps to explain the large piezoelectricity obtained at the morphotropic phase boundaries of these quadruple point based systems.

Current-induced phase transition of moving vortices in untwinned YBa2Cu3O7−δ single crystals

To study the phase transition of vortices induced by current flow, the electrical resistivity and the voltage–current characteristic have been measured on untwinned YBa2Cu3O7−δ single crystals in a magnetic field parallel to the c axis. Near a first-order melting transition (FOMT) line, the well-known counterclockwise hysteresis of resistivity drop disappears completely above a certain current density while a novel clockwise hysteresis appears just below this resistivity drop. Moreover, the voltage–current characteristic does not show any Ohmic behavior as the current increases near the FOMT line. The obtained results are explained by the current-induced melting of the vortex lattice or smectic similar to an increase in the temperature or the magnetic field.

Quantum annealed criticality: A scaling description

Experimentally there exist many materials with first-order phase transitions at finite temperature that display quantum criticality. Classically, a strain-energy density coupling is known to drive first-order transitions in compressible systems, and here we generalize this Larkin-Pikin mechanism to the quantum case. We show that if the T=0 system lies above its upper critical dimension, the line of first-order transitions ends in a "quantum annealed critical point" where zero-point fluctuations restore the underlying criticality of the order parameter. The generalized Larkin-Pikin phase diagram is presented and experimental consequences are discussed.