Microcanonical Monte Carlo Simulations Research Articles

Ensemble inequivalence in a generalized XY model

In this paper, we propose a new generalized XY model with nearest-neighbor interaction which cannot be studied analytically. By adopting both the canonical Monte Carlo simulations and the microcanonical Monte Carlo simulations, the first-order phase transitions in both canonical ensemble and microcanonical ensemble are observed numerically, and the accurate phase-transition temperatures of the model with different parameters are given. From the distinct phase diagrams in two different ensembles, we conclude that the model we propose here exists as an ensemble equivalence.

Mpemba effect of a mean-field system: The phase transition time.

The counterintuitive phenomenon-that an initially hotter water freezes faster than initially cooler water-is named the "Mpemba effect." Although it has been known for centuries, the underlying mechanism remains unclear. Recently, the Mpemba effect rekindled the interest of researchers since several studies identified that it might occur in some Markovian systems, and a general statistical-physical Mpemba effect framework was correspondingly proposed. In our previous study [Z.-Y. Yang and J.-X. Hou, Phys. Rev. E 101, 052106 (2020)10.1103/PhysRevE.101.052106], we observed the non-Markovian Mpemba effect in a mean-field system (MFS), where the Mpemba effect originates from the back-reaction of the thermal reservoir. Naturally, the phase transition time is the key to the occurrence of the Mpemba effect, which, however, has not been quantitatively described. Following the direction of previous work, this study rigorously derives the phase transition time under different conditions, and quantitatively describes the mechanism of the non-Markovian Mpemba effect in a MFS. In addition, the validation of our theory was further verified via the microcanonical Monte Carlo simulation. An accurate description of the underlying mechanism of our proposed MFS facilitates the generalization of the Mpemba effect framework in statistical physics and may benefit in answering the riddle of the century, the original Mpemba effect in water.

Multiple metastable states in an off-lattice Potts model

The interactions between a group of components are commonly studied in several areas of science (social science, biology, material science, complex dynamical systems, among others) using the methods of thermodynamics and statistical mechanics. In this work we study the properties of the recently proposed off-lattice, two-dimensional Potts model (Davis et al., 2014), originally motivated by the dynamics of agent opinions, and which is described by a Hamiltonian obtained by a maximum entropy inference procedure. We performed microcanonical and canonical Monte Carlo simulations of the first-order phase transition in the model, revealing a caloric curve with metastable regions. Furthermore, we report a “switching” behavior between multiple metastable states. We also note that the thermodynamics of the model has striking similarities with systems having long-range interactions, even though the interactions are short-ranged.

Computational statistical mechanics of a confined, three-dimensional Coulomb gas.

The thermodynamic properties of systems with long-range interactions present an ongoing challenge, from the point of view of both theory as well as computer simulation. In this paper we study a model system, a Coulomb gas confined inside a sphere, by using the Wang-Landau algorithm. We have computed the configurational density of states, the thermodynamic entropy, and the caloric curve, and compared with microcanonical Metropolis simulations, while showing how concepts such as the configurational inverse temperature can be used to understand some aspects of thermodynamic behavior. A dynamical multistability behavior is seen at low energies in microcanonical Monte Carlo simulations, suggesting that flat-histogram methods can in fact be useful and complementary alternatives to traditional Metropolis simulation in complex systems.

Violation of the Zeroth Law of Thermodynamics in a spin chain

A long-range interacting spin chain can exhibit temperature jump at the transition energy under the microcanonical description. After two identical long-range interacting subsystems of the same size at the same temperatures are weakly coupled, they exchange energy and the total microcanonical entropy of the full system increases irreversibly, leading to a violation of the Zeroth Law of Thermodynamics. In addition, microcanonical Monte Carlo simulations are performed to verify our conclusion.

Chain stiffness bridges conventional polymer and bio-molecular phases.

Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses-one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations, including a coil, a globule, a toroid, rods, helices, and zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffnesses play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.

Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking.

Spontaneous symmetry breaking (SSB) in statistical physics is a macroscopic collective phenomenon. For the paradigmatic Q-state Potts model it means a transition from the disordered color-symmetric phase to an ordered phase in which one color dominates. Existing mean field theories imply that SSB in the microcanonical statistical ensemble (with energy being the control parameter) should be a continuous process. Here we study microcanonical SSB on the random-graph Potts model and discover that the entropy is a kinked function of energy. This kink leads to a discontinuous phase transition at certain energy density value, characterized by a jump in the density of the dominant color and a jump in the microcanonical temperature. This discontinuous SSB in random graphs is confirmed by microcanonical MonteCarlo simulations, and it is also observed in bond-diluted finite-size lattice systems.

Microcanonical thermodynamics of three and four atoms.

Clusters are treated in the microcanonical ensemble. Two classical choices for the partition function are used in Boltzmann's assumption for entropy: Phase space volume and phase space density. For both definitions, exact statistical analogs are derived for energy derivatives of entropy to arbitrary order. The analogs are used in rigorous microcanonical Monte Carlo simulation to measure entropy derivatives up to order three for systems of three and four atoms. All simulation results are confirmed by direct numerical integration of the statistical analogs.

State transition and electrocaloric effect of BaZrxTi1−xO3: Simulation and experiment

We present a systematic study on the relation of the electrocaloric effect (ECE) and the relaxor state transition of BaZrxTi1−xO3 (BZT) using a combination of computer simulation and experiment. The results of canonical and microcanonical lattice-based Monte Carlo simulations with a Ginzburg-Landau-type Hamiltonian are compared with measurements of BaZrxTi1−xO3 (x = 0.12 and 0.2) samples. In particular, we study the ECE at various temperatures, domain patterns by piezoresponse force microscopy at room temperature, and the P-E loops at various temperatures. We find three distinct regimes depending on the Zr-concentration. In the compositional range 0≤x≤0.2, ferroelectric domains are visible, but the ECE peak drops considerably with increasing Zr-concentration. In the range 0.3≤x≤0.7, relaxor features become prominent, and the decrease in the ECE with Zr-concentration is moderate. In the range of high concentrations, x≥0.8, the material is almost nonpolar, and there is no ECE peak visible. Our results reveal that BZT with a Zr-concentration around x=0.12∼0.3 exhibits a relatively large ECE in a wide temperature range at rather low temperature.

Lattice-based Monte Carlo simulations of the electrocaloric effect in ferroelectrics and relaxor ferroelectrics

Canonical and microcanonical Monte Carlo simulations are carried out to study the electrocaloric effect (ECE) in ferroelectrics and relaxor ferroelectrics (RFEs) by direct computation of field-induced temperature variations at the ferroelectric-to-paraelectric phase transition and the nonergodic-to-ergodic state transformation. A lattice-based Hamiltonian is introduced, which includes a thermal energy, a Landau-type term, a dipole-dipole interaction energy, a gradient term representing the domain-wall energy, and an electrostatic energy contribution describing the coupling to external and random fields. The model is first parametrized and studied for the case of ${\mathrm{BaTiO}}_{3}$. Then, the ECE in RFEs is investigated, with particular focus on the influence of random fields and domain-wall energies. If the strength or the density of the random fields increases, the ECE peak shifts to a lower temperature but the temperature variation is reduced. On the contrary, if the domain-wall energy increases, the peak shifts to a higher temperature and the ECE becomes stronger. In RFEs, the ECE is maximum at the freezing temperature where the nonergodic-to-ergodic transition takes place. Our results imply that the presence of random fields reduces the entropy variation in an ECE cycle by pinning local polarization.

Maximum entropy reconstruction of the configurational density of states from microcanonical simulations

In this work we develop a method for inferring the underlying configurational density of states of a molecular system by combining information from several microcanonical molecular dynamics or Monte Carlo simulations at different energies. This method is based on Jaynes' Maximum Entropy formalism (MaxEnt) for Bayesian statistical inference under known expectation values. We present results of its application to measure thermodynamic entropy and free energy differences in embedded-atom models of metals.

Nature of First-Order Transition in Planar Rotator Model with Modified Potential

We have carried out micro-canonical Monte Carlosimulations of a planar rotator model in 30 × 30 lattice using periodic boundary conditions. The energy distribution of the rotator in the lattice shows features that can be associated with spin wave and vortex excitations. The results supplement the first-order transition observed in canonicalMonte Carlosimulation, due to vortex nucleation. We also see features that can be associated with the in-homogeneity of vortex charge in the critical region.

Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out in the citizen supercomputer Ibercivis. Upon dilution, the pure model's first-order transition becomes of the second-order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their Random Field Ising Model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.

Ensemble equivalence in spin systems with short-range interactions

We study the problem of ensemble equivalence in spin systems with short-rangeinteractions under the existence of a first-order phase transition. The spherical model withnonlinear nearest-neighbour interactions is solved exactly for both canonical andmicrocanonical ensembles. The result reveals apparent ensemble inequivalence at thefirst-order transition point in the sense that the microcanonical entropy is non-concave as afunction of the energy and consequently the specific heat is negative. In orderto resolve the paradox, we show that an unconventional saddle point should bechosen in the microcanonical calculation that represents a phase separation. TheXY model with nonlinear interactions is also studied by microcanonical Monte Carlosimulations in two dimensions to see how this model behaves in comparison with thespherical model.

Magnetic properties of ternary Prussian Blue Analogs studied with genetic approach

There are some similarities between the formulation of numerous magnetic problems and the description of Genetic Algorithm (GA) representations and operators. In the paper we use GA to determine the ground-states of Prussian Blue Analog AB p C 1− p . The structure of this molecular magnet is formed by two interpenetrating sublattices: the first one consists of atoms A and vacancies, the second one consists of B and C atoms where p factor describes the stoichiometry. The interaction model includes nearest neighbor interactions and the single-ion anisotropy. Such a sample has already been the subject of study [1] with some approximated model. Using our approach we obtained in some regions of phase diagram configurations which are energetically better than known before. The thermodynamical analysis was performed using the specific algorithm of microcanonical Monte Carlo simulation, namely Creutz demon technique. It shows only small changes in the shape of the ferri-paramagnetic phase transition curve.

Separation and fractionation of order and disorder in highly polydisperse systems

We study a polydisperse soft-spheres model for colloids by means of microcanonical Monte Carlo simulations. We consider a polydispersity as high as 24%. Although solidification occurs, neither a crystal nor an amorphous state are thermodynamically stable. A finite size scaling analysis reveals that in the thermodynamic limit: (a) the fluid-solid transition is rather a crystal-amorphous phase-separation, (b) such phase-separation is preceded by the dynamic glass transition, and (c) small and big particles arrange themselves in the two phases according to a complex pattern not predicted by any fractionation scenario.

Structural transitions and dipole moment of water clusters (H2O)n=4–100

The properties of water clusters (H(2)O)(n) over a broad range of sizes (n=4-100) were studied by microcanonical parallel tempering Monte Carlo and replica exchange molecular dynamics simulations at temperatures between 20 and 300 K, with special emphasis in the understanding of relation between the structural transitions and dipole behavior. The effect of the water interaction potential was analyzed using six nonpolarizable models, but more extensive calculations were performed using the TIP4P-ice water model. We find that, in general, the dipole moment of the cluster increases significantly as the cluster melts, suggesting that it could be used to discriminate between the solidlike and liquidlike phases. The effect of a moderate electric field on the cluster heat capacity and total dipole moment was found to be negligible.

Intrinsic electrocaloric effect in ferroelectric alloys from atomistic simulations

Electrocaloric effect (ECE) in $({\text{Ba}}_{0.5}{\text{Sr}}_{0.5}){\text{TiO}}_{3}$ ferroelectric alloys is calculated from first principles using a computational scheme that combines canonical and microcanonical Monte Carlo simulations. Our results are in very good agreement with the available experimental data and reveal many intriguing features of ECE including; (i) a significant enhancement of the ECE in paraelectric phase, (ii) nearly linear reversible temperature change associated with the electric field variation up to extremely large fields and, (iii) a possibility of achieving large ECE at room temperatures. Our atomistic insight suggests that in ferroelectrics ECE is caused by the redistribution of the entropy between the part associated with the dipoles' order and the part associated with the order in the kinetic energies of atomic vibrations. This mechanism can also be viewed as a ``conversion'' of spatially inhomogeneous dipole distribution into spatially inhomogeneous temperature distribution.

Phase transition in finite systems of 3D planar spin model with modified potential

We have studied the 3D planar spin model with modified potential using micro-canonical Monte Carlo simulations. For the first time, we have determined the value of q to be ⩾7.5 for the system to undergo a first-order transition. We have determined the negative specific heat and transition width as a function of system size at the first-order transition. The results have been compared with that of 2D Potts model and the 2D planar spin model with modified potential. The negative specific heat and the transition width at the first-order transition are found to be almost constant with increase in system size; unlike the 2D systems. The results have been understood qualitatively, in terms of order parameter correlation radius and correlation function.

Canonical and microcanonical Monte Carlo simulations of lattice-gas mixtures

We propose strict canonical and microcanonical Monte Carlo algorithms for an arbitrary lattice-gas binary mixture. We deduce formulas that allow us to obtain field quantities over the ensembles in which their conjugate extensive quantities are conserved. As an example, we have considered a lattice-gas mixture that is equivalent to the spin-1 Blume-Emery-Griffiths model [Phys. Rev. A 4, 1071 (1971)]. For a finite system and near a phase coexistence, the field as a function of its extensive conjugate shows a loop that disappears in the thermodynamic limit giving rise to the usual tie line. The first-order phase transition was determined by the use of three criteria.