Ising Universality Class Research Articles

Phase behavior of metastable water from large-scale simulations of a quantitatively accurate model near ambient conditions: The liquid-liquid critical point.

The molecular mechanisms of water's unique anomalies are still debated upon. Experimental challenges have led to simulations suggesting a liquid-liquid (LL) phase transition, culminating in the supercooled region's LL critical point (LLCP). Computational expense, small system sizes, and the reliability of water models often limit these simulations. We adopt the CVF model, which is reliable, transferable, scalable, and efficient across a wide range of temperatures and pressures around ambient conditions. By leveraging the timescale separation between fast hydrogen bonds and slow molecular coordinates, the model allows a thorough exploration of the metastable phase diagram of liquid water. Using advanced numerical techniques to bypass dynamical slowing down, we perform finite-size scaling on larger systems than those used in previous analyses. Our study extrapolates thermodynamic behavior in the infinite-system limit, demonstrating the existence of the LLCP in the 3D Ising universality class in the low-temperature, low-pressure side of the line of temperatures of maximum density, specifically at TC = 186 ± 4 K and PC = 174 ± 14 MPa, at the end of a liquid-liquid phase separation stretching up to ∼200 MPa. These predictions align with recent experimental data and sophisticated models, highlighting that hydrogen bond cooperativity governs the LLCP and the origin of water anomalies. We also observe substantial cooperative fluctuations in the hydrogen bond network at scales larger than 10nm, even at temperatures relevant to biopreservation. These findings have significant implications for nanotechnology and biophysics, providing new insights into water's behavior under varied conditions.

How motility affects Ising transitions

Abstract We study a lattice gas (LG) model of hard-core particles on a square lattice experiencing nearest neighbour attraction J. Each particle has an internal orientation, independent of the others, that point towards one of the four nearest neighbour and it can move to the neighbouring site along that direction with the usual metropolis rate if the target site is vacant. The internal orientation of the particle can also change to any of the other three with a constant rate ω . The dynamics of the model in ω → ∞ reduces to that of the LG which exhibits a phase separation transition at particle density ρ = 1 2 and temperature T = 1 , when the strength of attraction J crosses a threshold value ln ⁡ ( 1 + 2 ) . This transition belongs to Ising universality class (IUC). For any finite ω > 0 , the particles can be considered as attractive run-and-tumble particles (RTPs) in two dimensions with motility ω − 1 . We find that RTPs also exhibit a phase separation transition, but the critical interaction required is J c ( ω ) which increases monotonically with increased motility ω − 1 . It appears that the transition belongs to IUC. Surprisingly, in these models, motility impedes cluster formation process necessitating higher interaction to stabilize microscopic clusters. Moreover, MIPS like phases are not found when J = 0.

Tensor renormalization group study of (1 + 1)-dimensional U(1) gauge-Higgs model at θ = π with Lüscher’s admissibility condition

We investigate the phase structure of the (1+1)-dimensional U(1) gauge-Higgs model with a θ term, where the U(1) gauge action is constructed with Lüscher’s admissibility condition. Using the tensor renormalization group, both the complex action problem and topological freezing problem in the standard Monte Carlo simulation are avoided. We find the first-order phase transition with sufficiently large Higgs mass at θ = π, where the ℤ2 charge conjugation symmetry is spontaneously broken. On the other hand, the symmetry is restored with a sufficiently small mass. We determine the critical endpoint as a function of the Higgs mass parameter and show the critical behavior is in the two-dimensional Ising universality class.

The surface tension of Martini 3 water mixtures.

The Martini model, a coarse-grained forcefield for biomolecular simulations, has experienced a vast increase in popularity in the past decade. Its building-block approach balances computational efficiency with high chemical specificity, enabling the simulation of organic and inorganic molecules. The modeling of coarse-grained beads as Lennard-Jones particles poses challenges for the accurate reproduction of liquid-vapor interfacial properties, which are crucial in various applications, especially in the case of water. The latest version of the forcefield introduces refined interaction parameters for water beads, tackling the well-known artifact of Martini water freezing at room temperature. In addition, multiple sizes of water beads are available for simulating the solvation of small cavities, including the smallest pockets of proteins. This work focuses on studying the interfacial properties of Martini water, including surface tension and surface thickness. Employing the test-area method, we systematically compute the liquid-vapor surface tension across various combinations of water bead sizes and for temperatures from 300 to 350K. These findings are of interest to the Martini community as they allow users to account for the low interfacial tension of Martini water by properly adjusting observables computed via coarse-grained simulations to allow for accurate matching against all-atom or experimental results. Surface tension data are also interpreted in terms of local enrichment of the various mixture components at the liquid-vapor interface by means of Gibbs' adsorption formalism. Finally, the critical scaling of the Martini surface tension with temperature is reported to be consistent with the critical exponent of the 3D Ising universality class.

Independence role in the generalized Sznajd model

The Sznajd model is one of sociophysics’s well-known opinion dynamics models. Based on social validation, it has found application in diverse social systems and remains an intriguing subject of study, particularly in scenarios where interacting agents deviate from prevailing norms. This paper investigates the generalized Sznajd model, featuring independent agents on a complete graph and a two-dimensional square lattice. Agents in the network act independently with a probability p, signifying a change in their opinion or state without external influence. This model defines a paired agent size r, influencing a neighboring agent size n to adopt their opinion. This study incorporates analytical and numerical approaches, especially on the complete graph. Our results show that the macroscopic state of the system remains unaffected by the neighbor size n but is contingent solely on the number of paired agents r. Additionally, the time required to reach a stationary state is inversely proportional to the number of neighboring agents n. For the two-dimensional square lattice, two critical points p=pc emerge based on the configuration of agents. The results indicate that the universality class of the model on the complete graph aligns with the mean-field Ising universality class. Furthermore, the universality class of the model on the two-dimensional square lattice, featuring two distinct configurations, is identical and falls within the two-dimensional Ising universality class.

Quantifying nonuniversal corner free-energy contributions in weakly anisotropic two-dimensional critical systems.

We derive an exact formula for the corner free-energy contribution of weakly anisotropic two-dimensional critical systems in the Ising universality class on rectangular domains, expressed in terms of quantities that specify the anisotropic fluctuations. The resulting expression agrees with numerical exact calculations that we perform for the anisotropic triangular Ising model and quantifies the nonuniversality of the corner term for anisotropic critical two-dimensional systems. Our generic formula is expected to apply also to other weakly-anisotropic critical two-dimensional systems that allow for a conformal field theory description in the isotropic limit. We consider the three-states and four-states Potts models as further specific examples.

Theory of thermoreversible gelation and anomalous concentration fluctuations in polyzwitterion solutions.

We present a theoretical framework to investigate thermoreversible phase transitions within polyzwitterion systems, encompassing macrophase separations (MPS) and gelation. In addition, we explore concentration fluctuations near critical points associated with MPS, as well as tricritical and bicritical points at the intersection of MPS and gelation. By utilizing mean-field percolation theory and field theory formalism, we derive the Landau free energy in terms of polyzwitterion concentration with fixed dipole strengths and other experimental variables, such as temperatures and salt concentrations. As the temperature decreases, the dipoles can form cross-links, resulting in polyzwitterion associations. The associations can grow to a gel network and enhance the propensity for MPS, including liquid-liquid, liquid-gel, and gel-gel phase separations. Remarkably, the associations also impact critical behaviors. Using the renormalization group technique, we find that the critical exponents of the polyzwitterion concentration correlation functions significantly deviate from those in the Ising universality class due to the presence of polyzwitterion associations, leading to crossover critical behaviors.

Quantum Monte Carlo simulation of the 3D Ising transition on the fuzzy sphere

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional SU(2) layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

Thermodynamic crossovers in supercritical fluids

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid-gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, many existing theoretical explanations consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable, and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions.

Critical behavior of the dimerized Si(001) surface: Continuous order-disorder phase transition in the two-dimensional Ising universality class

Critical behavior of the dimerized Si(001) surface: Continuous order-disorder phase transition in the two-dimensional Ising universality class

Protecting information via probabilistic cellular automata.

Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature T, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic field h. In this article, we study a recently introduced probabilistic cellular automaton, the sweep rule, and map out a region of two coexisting stable phases in the (T,h) plane. We also find that the sweep rule belongs to the weak two-dimensional Ising universality class. Our work is a step towards understanding how simple geometrically local error-correction strategies can protect information encoded into complex noisy systems, such as topological quantum error-correcting codes.

Molecular Dynamics simulations and discrete perturbation theory for systems interacting via the parabolic-well pair potential

In this work, we performed Molecular Dynamics (MD) simulations to investigate the thermodynamic properties, including vapor pressures, critical points, pressure, excess energy, and vapor-liquid equilibrium, for a continuous version of the parabolic-well (PW) pair potential within the attractive range of 1.5 ≤λ≤3.0. In addition to conducting extensive MD simulations, we have developed an analytical equation of state for the Helmholtz free energy of particles interacting via the PW pair potential. This development was accomplished within the framework of discrete perturbation theory, involving discrete steps to accurately represent the general shape of the PW potential. Remarkably, our theoretical approach based on discrete perturbation theory demonstrates excellent agreement with MD simulations across a wide range of densities, temperatures, and pressures for the PW pair potential. Our findings demonstrate that PW fluids, characterized by long-range attractive interactions, deviate from the principle of corresponding states. However, for short-range attractive interactions, the fluids moderately follow the Ising universality class. Finally, the integration of discrete perturbation theory with MD simulations proves to be an efficient method for exploring the behavior of molecular fluids and colloidal systems.

Designer pair statistics of disordered many-particle systems with novel properties.

The knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing database of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform, and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperatures that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve many-particle systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics.

Transformation of the crystal structure of Ni0.5TiSe2 under in situ heating.

The crystal structure of the Ni0.5TiSe2 compound has been studied in situ in the temperature range of 25-1000 °C using synchrotron radiation X-ray diffraction. The previously known order-disorder transition in the Ni sublattice at ∼100 °C was found to be a second-order phase transition and belongs to the 3D Ising universality class. Reversible extraction of nickel selenides was observed in the temperature range of 275-975 °C. It was explained in terms of Ni extraction from Ni0.5TiSe2 due to the thermal widening of the Ni 3d/Ti 3d/Se 4p impurity band. The Ni-TiSe2 phase diagram follows the typical pattern of MxTiSe2 (M - transition metal) compounds.

Characterizing quantum criticality in the transverse field Ising model with staggered Dzyaloshinskii–Moriya interaction

The quantum criticality and entanglement properties are investigated in the one-dimensional spin-1/2 transverse field Ising model with staggered Dzyaloshinskii–Moriya interaction by utilizing the infinite-time evolving block decimation method. In this model, the staggered Dzyaloshinskii–Moriya interaction does not lead any new phase, while it only appears a phase transition line between Néel phase and paramagnetic phase. The behaviors of measurements of information illustrate the quantum phase transition and the existence of factorized points. The factorization phenomena is observed in the transverse Néel phase detecting by the entanglement quantities, in which the double degenerate ground state in transverse Néel phase is preserved by the Dzyaloshinskii–Moriya interaction also evidencing from the fidelity map. From the perspective of magnetism, the existence of chiral order and transverse Néel order suggests the helical magnetic structure induced by Dzyaloshinskii–Moriya interaction. The critical exponents and central charge keep invariant and convinced that the phase transitions belong to the Ising universality class. In contrary to the systems confined within central charge c=1, although the competition between the Dzyaloshinskii–Moriya interaction and external field changes the phase transition and entanglement properties, the quantum criticality seems independent of Dzyaloshinskii–Moriya interaction.

Unraveling the magnetic properties and nature of exchange interactions of Mn5−x Fe x Ge3 (0.15 ≤ x ≤ 0.5) alloys

We report the structural and magnetic properties of arc-melted Fe-doped Mn5Ge3 alloys. In this study, Mn5−x Fe x Ge3 (x = 0.15, 0.3, and 0.5) alloys were subjected to DC magnetic measurements in order to examine the nature of magnetic interaction via critical exponents study in the asymptotic critical region. The critical exponents β, γ and δ are obtained independently from different methods. For Mn4.85Fe0.15Ge3, β = 0.338, γ = 1.146 and δ = 4.39; for Mn4.7Fe0.3Ge3, β = 0.337, γ = 1.244 and δ = 4.69 and for Mn4.5Fe0.5Ge3, β = 0.328, γ = 1.195 and δ = 4.64. The values of critical exponents obtained are found to be close to the 3D Ising universality class (β = 0.325, γ = 1.241, and δ = 4.82). Analyses based on the Renormalization group theory predictions reveal that the spin interactions are short-range extended types beyond the nearest neighbors due to the presence of a different set of Mn–Mn interactions with an unequal magnitude of exchange strengths in the Mn5−x Fe x Ge3 alloys.

Liquid−vapor order parameter and coexistence-curve diameter of nitrogen, ethylene, and sulfur hexafluoride: From the triple point to the critical scaling regime

Analytic closed-form expressions are obtained for the liquid and vapor saturation densities defining the coexistence curve. The densities are modeled with broken power laws and Weibull distributions. Specifically, the coexistence curves of nitrogen, ethene and sulfur hexafluoride are derived, without the use of perturbative expansions, based on high-precision data extending from the triple point into the critical regime. The analytic continuation of the vapor branch below the triple point decays exponentially at low temperature. The order parameter and coexistence-curve diameter of the fluids are assembled from the regressed liquid and vapor branches of the coexistence curve, and the critical power-law scaling of these quantities is examined. The scaling exponents of the order parameter and the reduced diameter are regressed and compared with the calculated critical exponents of the 3D Ising universality class. Index functions representing the Log−Log slopes (temperature-dependent effective exponents) of the liquid and vapor densities, order parameter and diameter are used to determine the onset of the ideal power-law scaling regime and to illustrate the slope evolution of these quantities in the subcritical regime.

Critical behavior in a chiral molecular model.

Understanding the condensed-phase behavior of chiral molecules is important in biology as well as in a range of technological applications, such as the manufacture of pharmaceuticals. Here, we use molecular dynamics simulations to study a chiral four-site molecular model that exhibits a second-order symmetry-breaking phase transition from a supercritical racemic liquid into subcritical D-rich and L-rich liquids. We determine the infinite-size critical temperature using the fourth-order Binder cumulant, and we show that the finite-size scaling behavior of the order parameter is compatible with the 3D Ising universality class. We also study the spontaneous D-rich to L-rich transition at a slightly subcritical temperature of T = 0.985Tc, and our findings indicate that the free energy barrier for this transformation increases with system size as N2/3, where N is the number of molecules, consistent with a surface-dominated phenomenon. The critical behavior observed herein suggests a mechanism for chirality selection in which a liquid of chiral molecules spontaneously forms a phase enriched in one of the two enantiomers as the temperature is lowered below the critical point. Furthermore, the increasing free energy barrier with system size indicates that fluctuations between the L-rich and D-rich phases are suppressed as the size of the system increases, trapping it in one of the two enantiomerically enriched phases. Such a process could provide the basis for an alternative explanation for the origin of biological homochirality. We also conjecture the possibility of observing nucleation at subcritical temperatures under the action of a suitable chiral external field.

Topological and quantum critical properties of the interacting Majorana chain model

We study Majorana chain with the shortest possible interaction term and in the presence of hopping alternation. When formulated in terms of spins the model corresponds to the transverse field Ising model with nearest-neighbor transverse and next-nearest-neighbor longitudinal repulsion. The phase diagram obtained with extensive DMRG simulations is very rich and contains six phases. Four gapped phases include paramagnetic, period-2 with broken translation symmetry, \mathbb{Z}_2ℤ2 with broken parity symmetry and the period-2-\mathbb{Z}_2ℤ2 phase with both symmetries broken. In addition there are two floating phases: gapless and critical Luttinger liquid with incommensurate correlations, and with an additional spontaneously broken \mathbb{Z}_2ℤ2 symmetry in one of them. By analyzing an extended phase diagram we demonstrate that, in contrast with a common belief, the Luttinger liquid phase along the self-dual critical line terminates at a weaker interaction strength than the end point of the Ising critical line that we find to be in the tri-critical Ising universality class. We also show that none of these two points is a Lifshitz point terminating the incommensurability. In addition, we analyzed topological properties through Majorana zero modes emergent in the two topological phases, with and without incommensurability. In the weak interaction regime, a self-consistent mean-field treatment provides a remarkable accuracy for the description of the spectral pairing and the parity switches induced by the interaction.

Static universality of the Ising and Blume–Capel models on two-dimensional Penrose tiles

We study the phase transitions and the critical behavior of the Ising and Blume–Capel models on two kinds of two-dimensional Penrose tiles employing Monte Carlo methods and detailed finite-size scaling analysis. The Wolff algorithm is used for the Ising model whereas the Wang–Landau and Metropolis algorithms are used for the Blume–Capel model to obtain critical temperatures and exponents. The phase diagram of the Blume–Capel model reveals the presence of the double transition, the reentrant behavior, and the tricriticality in the vicinity of the critical single-ion anisotropy. Our results indicate that continuous phase transitions of the Ising and Blume–Capel models on the Penrose tiles belong to the two-dimensional Ising universality class. However, the scaling functions depend on the spin magnitude, anisotropy, and graph shape. Lastly, we verify that the critical Binder cumulant is also universal but depends on the shape of the graph.