Full Phase Diagram Research Articles

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

Magnetic phase diagram and possible Kitaev-like behavior of the honeycomb-lattice antimonate Na3Co2SbO6

Recent theoretical studies have suggested that Kitaev physics and such effects as formation of a mysterious spin-liquid state can be expected not only in RuCl3 and iridates, but also in conventional $3d$ transition metal compounds. Using DC and AC magnetometry, thermodynamic and $^{23}$Na nuclear magnetic resonance measurements (NMR) we studied such a candidate material Na3Co2SbO6. A full phase diagram of Na3Co2SbO6 in a wide range of magnetic fields and temperatures is presented. The results demonstrate transformation of the antiferromagnetic structure under the external magnetic field, gradual development of the saturation phase, as well as evidence of gapped behavior in certain parts of the phase diagram

Solid-liquid transition induced by rigidity disparity in a binary mixture of cell tissues.

The two-dimensional melting of a binary mixture of cell tissues is numerically investigated in the presence of rigidity disparity. We present the full melting phase diagrams of the system by using the Voronoi-based cellular model. It is found that the enhancement of rigidity disparity can induce a solid-liquid transition at both zero temperature and finite temperature. (i) In the case of zero temperature, the system undergoes a continuous solid-hexatic transition followed by a continuous hexatic-liquid transition for zero rigidity disparity, but a discontinuous hexatic-liquid transition for finite rigidity disparity. Remarkably, the solid-hexatic transitions always arise when the soft cells reach the rigidity transition point of monodisperse systems. (ii) In the case of finite temperature, the melting occurs via a continuous solid-hexatic transition followed by a discontinuous hexatic-liquid transition. Our study may contribute to the understanding of solid-liquid transitions in binary mixture systems with rigidity disparity.

Effect of Disparity in Self Dispersion Interactions on Phase Behaviors of Molten A-b-B Diblock Copolymers.

Phase behaviors of molten A-b-B diblock copolymers with disparity in self dispersion interactions are revisited here. A free energy functional is obtained for the corresponding Gaussian copolymers under the influence of effective interactions originating in the localized excess equation of state. The Landau free energy expansion is then formulated as a series in powers of A and B density fluctuations up to 4th order. An alternative and equivalent Landau energy is also provided through the transformation of the order parameters to the fluctuations in block density difference and free volume fraction. The effective Flory χ is elicited from its quadratic term as the sum of the conventional enthalpic χH and the entropic χS that is related to energetic asymmetry mediated by copolymer bulk modulus. It is shown that the cubic term is balanced with Gaussian cubic vertex coefficients in corporation with energetics to yield a critical point at a composition rich in a component with stronger self interactions. The full phase diagrams with classical mesophases are given for the copolymers exhibiting ordering upon cooling and also for others revealing ordering reversely upon heating. These contrasting temperature responses, along with the skewness of phase boundaries, are discussed in relation to χH and χS. The pressure dependence of their ordering transitions is either barotropic or baroplastic; or anomalously exhibits anomalously both at different stages. These actions are all explained by the opposite responses of χH and χS to pressure.

High-pressure investigations in CH3NH3PbX3 ( X = I, Br, and Cl): Suppression of ion migration and stabilization of low-temperature structure

Hybrid organic-inorganic halide perovskites represent a promising next-generation photovoltaic material with drawbacks for structure stability and composition concerns. Demonstrations of ion migration and molecular dynamics suggest room for structural contraction and subsequent property adjustments. Here, we deploy dielectric and infrared spectroscopy under external pressure to probe the full structural phase diagram and dielectric response of methylammonium lead halide perovskites ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}\mathrm{Pb}{X}_{3}$ ($X\phantom{\rule{4pt}{0ex}}=$ I, Br, or Cl). Ion migration can be fully suppressed by pressure beyond 4 GPa. The low-temperature orthorhombic phase transition can be gradually enhanced and stabilized at ambient conditions with increasing pressure. A slow relaxation mode, presumably the motion of the ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}^{+}$ cation, is observed at lower pressure and is absent in the orthorhombic phase for every halide.

Multicomponent Chiral Quantification with Ultraviolet Circular Dichroism Spectroscopy: Ternary and Quaternary Phase Diagrams of Levetiracetam.

Chiral molecules are challenging for the pharmaceutical industry because although physical properties of the enantiomers are the same in achiral systems, they exhibit different effects in chiral systems, such as the human body. The separation of enantiomers is desired but complex, as enantiomers crystallize most often as racemic compounds. A technique to enable the chiral separation of racemic compounds is to create an asymmetry in the thermodynamic system by generating chiral cocrystal(s) using a chiral coformer and using the solubility differences to enable separation through crystallization from solution. However, such quaternary systems are complex and require analytical methods to quantify different chiral molecules in solution. Here, we develop a new chiral quantification method using ultraviolet-circular dichroism spectroscopy and multivariate partial least squares calibration models, to build multicomponent chiral phase diagrams. Working on the quaternary system of (R)- and (S)-2-(2-oxopyrrolidin-1-yl)butanamide enantiomers with (S)-mandelic acid in acetonitrile, we measure accurately the full quaternary phase diagram for the first time. By understanding the phase stabilities of the racemic compound and the enantiospecific cocrystal, the chiral resolution of levetiracetam could be designed due to a large asymmetry in overall solubility between both sides of the racemic composition. This new method offers improvements for chiral molecule quantification in complex multicomponent chiral systems and can be applied to other chiral spectroscopy techniques.

Ab initio construction of full phase diagram of MgO-CaO eutectic system using neural network interatomic potentials

While several studies confirmed that machine-learned potentials (MLPs) can provide accurate free energies for determining phase stabilities, the abilities of MLPs for efficiently constructing a full phase diagram of multicomponent systems are yet to be established. In this work, by employing neural network interatomic potentials (NNPs), we demonstrate construction of the MgO-CaO eutectic phase diagram with temperatures up to 3400 K, which includes liquid phases. The NNP is trained over trajectories of various solid and liquid phases at several compositions that are calculated within the density functional theory (DFT). For the exchange-correlation energy among electrons, we compare the PBE and SCAN functionals. The phase boundaries such as solidus, solvus, and liquidus are determined by free energy calculations based on the thermodynamic integration or semigrand ensemble methods, and salient features in the phase diagram such as solubility limit and eutectic points are well reproduced. In particular, the phase diagram produced by the SCAN-NNP closely follows the experimental data, exhibiting both eutectic composition and temperature within the measurements. On a rough estimate, the whole procedure is more than 1000 times faster than pure-DFT based approaches. We believe that this work paves the way to fully ab initio calculation of phase diagrams.

Ultra-Rapid, Physics-Based Development Pathway for Reactor-Relevant RF Antenna Materials

This article presents a rapid, atomistically informed, experimental development pathway for fusion reactor-relevant radio-frequency (RF) antenna materials in the Cu-Cr-(Nb,Al,Zr) composition system, with the goal of improving upon GRCop-84. RF antennas in a tokamak fusion reactor will face a unique set of challenges as both structural and functional materials. The desired material must simultaneously achieve and maintain high electrical conductivity, high strength, high thermal conductivity, resist high temperatures, possess low nuclear activation, and incur low damage due to neutron bombardment. The GRCop-84 alloy serves as a starting point for iterative improvement, with the desire to reduce or eliminate Nb from the material to minimize nuclear activation. The rapid development pathway makes use of a multi-target combinatorial thick-film sputtering process to produce full ternary phase diagrams on a Si wafer substrate. Transient grating spectroscopy (TGS), a laser-ultrasonic method, will determine spatially varying thermoelastic properties, while four terminal electrical conductivity measurements will map out the best performing regions of the sample for in-depth study at larger length scales. High-energy proton and self-ion irradiation emulates the effects of neutron damage on the thermal/electric properties. With rapid turnaround time (~days) in terms of mapping radiation damage-induced material property changes in the full ternary system, these techniques allow rapid iteration toward an optimal material, testing hundreds of nearby compositions in the time it took to test one. Focused testing of larger, single composition samples (produced in an arc furnace or by laser sintering) provides data on structural and high-power RF properties and validates our thick-film-based workflow.

Topological transitions in magnetized plasma and optical isolators based on leaky waveguide plasmon mode

Topological transitions open a fundamentally new route of research with interesting optical phenomena in photonic metamaterials. In this work, we comprehensively investigate the topology of equifrequency surfaces in magnetized plasma. The full topological phase diagrams are shown and the critical points in the topological transitions are given. The equifrequency surfaces evolve from the closed-form ellipsoid to the open forms type-I or type-II hyperboloid in the topological transitions. Remarkably, a type of nonreciprocal optical isolator is demonstrated utilizing the transformation from topological surface states to leaky modes in magnetized plasma. Our work may provide additional insights into topological wave physics and the novel optical isolator has potential applications in light modulation.

Low-energy prethermal phase and crossover to thermalization in nonlinear kicked rotors

In the presence of interactions, periodically-driven quantum systems generically thermalize to an infinite-temperature state. Recently, however, it was shown that in random kicked rotors with local interactions, this long-time equilibrium could be strongly delayed by operating in a regime of weakly fluctuating random phases, leading to the emergence of a metastable thermal ensemble. Here we show that when the random kinetic energy is smaller than the interaction energy, this system in fact exhibits a much richer dynamical phase diagram, which includes a low-energy pre-thermal phase characterized by a light-cone spreading of correlations in momentum space. We develop a hydrodynamic theory of this phase and find a very good agreement with exact numerical simulations. We finally explore the full dynamical phase diagram of the system and find that the transition toward full thermalization is characterized by relatively sharp crossovers.

Metastability for expanding bubbles on a sticky substrate

We study the dynamical behavior of a one dimensional interface interacting with a sticky impenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contacts between the interface and the substrate are given an energetic bonus while an external force with constant intensity pulls the interface away from the wall. Our interface is modeled by the graph of a one-dimensional nearest-neighbor path on Z+, starting at 0 and ending at 0 after 2N steps, with the wall being the horizontal axis. At equilibrium each path ξ=(ξx)x=02N is given a probability proportional to λH(ξ)exp(σNA(ξ)), where H(ξ):=#{x:ξx=0} and A(ξ) is the area enclosed between the path ξ and the x-axis. We then consider the classical heat-bath dynamics which equilibrates the value of each ξx at a constant rate via corner-flip. Investigating the statics of the model, we derive the full phase diagram in λ and σ of this model, and identify the critical line which separates a localized phase where the pinning force sticks the interface to the wall and a delocalized one, for which the external force stabilizes ξ around a deterministic shape at a macroscopic distance of the wall. On the dynamical side, we identify a second critical line, which separates a rapidly mixing phase (for which the system mixes in polynomial time) to a slow phase where the mixing time grows exponentially. In this slowly mixing regime, we obtain a sharp estimate of the mixing time on the log scale, and provide evidences of a metastable behavior.

Studying the Structure of Sodium Lauryl Ether Sulfate Solutions Using Dissipative Particle Dynamics.

Sodium lauryl ether sulfate (SLES) is a common anionic surfactant used in a large number of personal care products. Commercial products typically contain a distribution in the number of ethoxy groups; despite this, there is limited existing work studying the effect of the ethoxy groups on the phase formation and structure. This is particularly important for the effect the structure has on the viscosity, an important consideration for commercial products. Dissipative particle dynamics is used to simulate the full phase diagram of SLES in water, including both micellar and lyotropic liquid crystal phases. Phase transitions occur at locations which are in good agreement with experimental data, and we find that these boundaries can shift as a result of varying the number of ethoxy groups. Varying the ethoxy groups has a significant effect on the micellar shape and crystalline spacing, with a reduction leading to more nonspherical micelles and decreased periodic spacing of the hexagonal and lamellar phases. Finally, while typical commercial products contain a distribution of ethoxy groups, computational work tends to focus on simulations containing a single chain length. We show that it is valid to use monodisperse simulations to infer behavior about solutions with a polydisperse chain length, based on its mean molecular length.

Kinetic Phase Diagram for Nucleation and Growth of Competing Crystal Polymorphs in Charged Colloids.

We determine the kinetic phase diagram for nucleation and growth of crystal phases in a suspension of charged colloids. Exploiting the seeding approach in extensive simulations, we calculate nucleation barrier heights for face-centered cubic (fcc) and body-centered cubic (bcc) phases for varying screening lengths and supersaturations. We determine for the entire metastable fluid region the crystal polymorph with the lowest nucleation barrier, and find a regime close to the triple point where metastable bcc can form due to a lower nucleation barrier, even though fcc is the stable phase. For higher supersaturation, we find that the difference in barrier heights decreases and we observe a mix of hexagonal close-packed, fcc, and bcc structures in the growth of crystalline seeds as well as in spontaneously formed crystals. Our kinetic phase diagram rationalizes the different crystallization mechanisms observed in previous work.

In silico study of liquid crystalline phases formed by bent-shaped molecules with excluded volume type interactions

What impact does the mesogens’ shape have on the formation of the liquid crystalline phase? Using Monte Carlo and molecular dynamics simulations we numerically studied a liquid composed of achiral, bent-shaped molecules built of tangent spheres. The system is known to spontaneously break mirror symmetry, as it forms a macroscopically chiral, twist-bend nematic phase [Phys. Rev. Lett. 115, 147801 (2015)]. We examined a full phase diagram by altering the molecules’ curvature along with packing fractions and observed several phases characterized by the orientational and/or translational ordering of molecules. Apart from conventional nematic, smectic A, and the aforementioned twist-bend nematic phase, we identified splay-bend smectic phase. For large densities and strongly curved molecules, another smectic phase emerged, where the polarization vector rotates within a single smectic layer.

Multipartite nonlocality and topological quantum phase transitions in a spinless fermion quantum wire with uniform and incommensurate potentials

Multipartite nonlocality and Bell-type inequalities are used to characterize topological quantum phase transitions (QPTs) in a spinless fermion quantum wire, where both uniform potentials and incommensurate potentials are considered. First, the nonlocality measures show clear signals at the critical points in both the uniform model and the incommensurate model. It indicates that these QPTs are accompanied by dramatic changes of multipartite quantum correlations in the ground states. Second, finite-size scaling analysis is carried out. In particular, in the incommensurate model where translation invariance is broken, with some rescaling techniques, we successfully establish the scaling formula in the large-$L$ limit. Finally, the full phase diagram of the model with mixed potentials is figured out. We find a region which is featured with strong randomness in the large-$L$ limit. The structure of this region is revealed by analyzing the energy spectrum, and an efficient approach to characterize this region is proposed.

Electron–phonon coupling constant and BCS ratios in LaH10−y doped with magnetic rare-earth element

Stoichiometric near-room-temperature superconductors (NRTS) (for instance, H3S and LaH10) exhibit a high ground-state upper critical field, B c2(0) ⩾ 100 T, so that the magnetic phase diagram in these materials cannot be measured in non-destructive experiments. However, (Semenok et al 2022 Adv. Mater.) proposed the idea of exploring the full magnetic phase diagram in NRTS samples, in which the superconducting order parameter is suppressed by magnetic element doping. If the elements areuniformly distributed in the material, then the theory of electron–phonon mediated superconductivity predicts the suppression of the order parameter in a 3D s-wave superconductor. (Semenok et al 2022 Adv. Mater.) experimentally proved this idea by substituting lanthanum with the magnetic rare-earth neodymium in (La1−x Nd x )H10−y . As a result, the transition temperature in (La1−x Nd x )H10−y (x = 0.09) was suppressed to T c ∼ 120 K, and the upper critical field decreased to B c2(T= 41 K) = 55 T. While the exact hydrogen content should be further established in the (La1−x Nd x )H10−y (x = 0.09) (because similar T c suppression was observed in hydrogen-deficient LaH10−y samples reported by Drozdov et al (2019 Nature 569 528)), a significant part of the full magnetic phase diagram for the (La1−x Nd x )H10−y (x = 0.09) sample was measured. Here, we analyzed the reported (Semenok et al 2022 Adv. Mater.) magnetoresistance data for (La1−x Nd x )H10−y (x = 0.09) compressed at P = 180 GPa and deduced: (a) Debye temperature, ; (b) the electron–phonon coupling constant, ; (c) the ground-state superconducting energy gap, ; (d) the gap-to-transition temperature ratio, ; and (e) the relative jump in specific heat at transition temperature, . The deduced values indicate that (La1−x Nd x )H10−y (x = 0.09; P = 180 GPa) is a moderately strongly coupled s-wave superconductor.

Measurement-induced phase transition in a chaotic classical many-body system

Local measurements in quantum systems are projective operations which act to counteract the spread of quantum entanglement. Recent work has shown that local, random measurements applied to a generic volume-law entanglement generating many-body system are able to force a transition into an area-law phase. This work shows that projective operations can also force a similar classical phase transition; we show that local projections in a chaotic system can freeze information dynamics. In rough analogy with measurement-induced phase transitions, this is characterized by an absence of information spreading instead of entanglement entropy. We leverage a damage-spreading model of the classical transition to predict the butterfly velocity of the system both near to and away from the transition point. We map out the full phase diagram and show that the critical point is shifted by local projections, but remains in the directed percolation universality class. We discuss the implication for other classical chaotic many-body systems.

Machine learning techniques to construct detailed phase diagrams for skyrmion systems

Recently, there has been an increased interest in the application of machine learning (ML) techniques to a variety of problems in condensed matter physics. In this regard, of particular significance is the characterization of simple and complex phases of matter. Here, we use a ML approach to construct the full phase diagram of a well known spin model combining ferromagnetic exchange and Dzyaloshinskii-Moriya (DM) interactions where topological phases emerge. At low temperatures, the system is tuned from a spiral phase to a skyrmion crystal by a magnetic field. However, thermal fluctuations induce two types of intermediate phases, bimerons and skyrmion gas, which are not as easily determined as spirals or skyrmion crystals. We resort to large scale Monte Carlo simulations to obtain low temperature spin configurations, and train a convolutional neural network (CNN), taking only snapshots at specific values of the DM couplings, to classify between the different phases, focusing on the intermediate and intricate topological textures. We then apply the CNN to higher temperature configurations and to other DM values, to construct a detailed magnetic field-temperature phase diagram, achieving outstanding results. We discuss the importance of including the disordered paramagnetic phases in order to get the phase boundaries, and finally, we compare our approach with other ML algorithms.

Spin functional renormalization group for dimerized quantum spin systems

We investigate dimerized quantum spin systems using the spin functional renormalization group approach proposed by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)] which directly focuses on the physical spin correlation functions and avoids the representation of the spins in terms of fermionic or bosonic auxiliary operators. Starting from decoupled dimers as initial condition for the renormalization group flow equations, we obtain the spectrum of the triplet excitations as well as the magnetization in the quantum paramagnetic, ferromagnetic, and thermally disordered phases at all temperatures. Moreover, we compute the full phase diagram of a weakly coupled dimerized spin system in three dimensions, including the correct mean field critical exponents at the two quantum critical points.

Effect of intrinsic quantum fluctuations on the phase diagram of anisotropic dipolar magnets

The rare-earth material $\mathrm{LiHoF_4}$ is believed to be an experimental realization of the celebrated (dipolar) Ising model, and upon the inclusion of a transverse field $B_x$, an archetypal quantum Ising model. Moreover, by substituting the magnetic Ho ions by non-magnetic Y ions, disorder can be introduced into the system giving rise to a dipolar disordered magnet and at high disorders to a spin-glass. Indeed, this material has been scrutinized experimentally, numerically and theoretically over many decades with the aim of understanding various collective magnetic phenomena. One of the to-date open questions is the discrepancy between the experimental and theoretical $B_x -T$ phase diagram at low-fields and high temperatures. Here we propose a mechanism, backed by numerical results, that highlights the importance of quantum fluctuations induced by the off-diagonal dipolar terms, in determining the critical temperature of anisotropic dipolar magnets in the presence and in the absence of a transverse field. We thus show that the description as a simple Ising system is insufficient to quantitatively describe the full phase diagram of $\mathrm{LiHoF_4}$, for the pure as well as for the dilute system.