Binder Cumulant Research Articles

Nonequilibrium tricritical behavior in anisotropic XY ferromagnet driven by elliptically polarized propagating magnetic field wave

The three-dimensional anisotropic XY ferromagnet, driven by an elliptically polarized propagating magnetic field wave, has been extensively investigated by Monte Carlo simulation with the Metropolis single spin flip algorithm. Both the effects of the bilinear exchange type and the single-site anisotropies are thoroughly investigated. The time-averaged magnetization (over the complete cycle of the elliptically polarized propagating magnetic field wave) components play the role of the dynamic order parameter. For a fixed set of values of the strength of anisotropy and the field amplitudes, the system has been found to get dynamically ordered at a pseudocritical temperature. The pseudocritical temperature of such a dynamic nonequilibrium phase transition has been found to depend both on the strength of anisotropy and the amplitudes of the elliptically polarized propagating magnetic field wave. A comprehensive phase diagram is represented here in the form of an image plot of the pseudocritical temperature in the plane formed by the strength of anisotropy and field amplitudes. Interestingly, this nonequilibrium phase transition has been found to be discontinuous (first order) for higher values of the field amplitude. On the other hand, the continuous (second order) transition has been noticed for lower values of the field amplitude. Such an interesting nonequilibrium tricritical behavior has been observed in driven XY ferromagnet. The order of such a nonequilibrium phase transition has been confirmed by the thermal variation (near the transition) of the statistical distribution of the order parameter and by the thermal variation of the fourth-order Binder cumulant. In the plane formed by field amplitude and anisotropy, a tricritical line has been shown as the accompanying (and complementary) phase diagram. The dependence of the pseudocritical temperature, on the frequency and wavelength of the elliptically polarized propagating magnetic field wave, has also been reported.

Blume-Capel model analysis with a microcanonical population annealing method.

We present a modification of the Rose-Machta algorithm [N. Rose and J. Machta, Phys. Rev. E 100, 063304 (2019)2470-004510.1103/PhysRevE.100.063304] and estimate the density of states for a two-dimensional Blume-Capel model, simulating 10^{5} replicas in parallel for each set of parameters. We perform a finite-size analysis of the specific heat and Binder cumulant, determine the critical temperature along the critical line, and evaluate the critical exponents. The obtained results are in good agreement with those previously obtained using various methods-Markov chain Monte Carlo simulation, Wang-Landau simulation, transfer matrix, and series expansion. The simulation results clearly illustrate the typical behavior of specific heat along the critical lines and through the tricritical point.

Quantum phases of spin-1/2 extended XY model in transverse magnetic field

In this study, a spin-1/2 extended anisotropic XY chain has been introduced in which both time reversal and SU(2) symmetries are broken but Z 2 symmetry is preserved. Magnetic and topological phase diagrams in the parameter space have been drawn in the presence of transverse magnetic field. Entanglement measures like mutual information and quantum discord are also evaluated and it indicates that these transitions are second order in nature. Quantum phase transition is noted at zero magnetic field, as well as magnetic long range order is found to withstand magnetic field of any strength. Exact analytic results for spin-spin correlation functions have been obtained in terms of Jordan-Wigner fermionization. Existence of long range magnetic order has been investigated numerically by finding correlation functions as well as the Binder cumulant in the ground state. Dispersion relation, ground state energy, and energy gap are obtained analytically. In order to find the topologically nontrivial phase, sign of Pfaffian invariant and value of winding number have been evaluated. Both magnetic and topological phases are robust against the magnetic field and found to move coercively in the parameter space with the variation of its strength. Long range orders along two orthogonal directions and two different topological phases are found and their one-to-one correspondence has been found. Finally casting the spinless fermions onto Majorana fermions, properties of zero energy edge states are studied. Three different kinds of Majorana pairings are noted. In the trivial phase, next-nearest-neighbor Majorana pairing is found, whereas two different types of nearest-neighbor Majorana pairings are identified in the topological superconducting phase.

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.

Fazovye perekhody v chasovoy modeli s chislom sostoyaniy spina <i>q </i>= 5 na treugol'noy reshetke

The phase transitions and thermodynamic properties of the clock model with q = 5 spin states on a triangular lattice have been investigated using the Wang–Landau Monte Carlo algorithm. The phase transitions have been analyzed with the histogram method and the fourth-order Binder cumulant method. Two Berezinskii–Kosterlitz–Thouless phase transitions are shown to be observed in the ferromagnetic clock model, while a second-order phase transition has been detected in the antiferromagnetic clock model.

Magnetic and magnetocaloric characteristics of the mixed Graphullerene-like structure: A theoretical study

This paper presents an investigation of the magnetic and magnetocaloric properties of a mixed Graphullerene-like nanostructure. The Blume–Capel model is employed, and Monte Carlo computations were performed using the Metropolis algorithm. The study examines various spin configurations within different parameter planes and reveals stable configurations. Furthermore, the paper analyzes magnetizations, susceptibilities, specific heat, and Binder cumulant as a function of the temperature to determine the transition temperature and characterize magnetic phase transitions in the system. The suitability of the investigated structure for magnetic refrigeration was also assessed by examining the magnetic entropy change and relative cooling power at different external magnetic field strengths. The results show a direct correlation between the external magnetic field and maximum entropy changes, indicating a significant magnetocaloric effect.

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.

Magnetic properties and magnetocaloric effects of the graphullerene-like 4-(Mg4C60) nanostructure: A Monte Carlo study

This work presents a study of the magnetic and magnetocaloric properties of mixed spins ([Formula: see text], [Formula: see text]) in a Graphullerene-like nanostructure. Monte Carlo simulations (MCs) were conducted using the Metropolis algorithm in the Blume–Capel model. The ground state phase diagrams were established and illustrated for different physical parameters. Additionally, the corresponding magnetizations, susceptibilities, specific heat, Binder cumulant, magnetic and change entropies were examined versus temperature. The critical temperature was determined, and hysteresis cycles were presented for specific physical parameter values. The results suggest that the structure shows potential as a candidate for magnetic refrigeration.

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.

New order parameter for the Higgs transition in SU(2) -Higgs theory

We investigate the Higgs transition within the four-dimensional $SU(2)$-Higgs model in search for an order parameter as a function of the Higgs field hopping parameter, $\ensuremath{\kappa}$, using lattice technique. We measure the Higgs condensate after applying Landau gauge fixing and study the corresponding susceptibility, magnetization, and fourth order Binder cumulant using four different spatial volumes with ${N}_{\ensuremath{\tau}}=2$. The computation is carried out with gauge coupling, ${\ensuremath{\beta}}_{g}=8$, for a range of scalar self-coupling, $\ensuremath{\lambda}={0.00010,0.00350}$, with an emphasis near the critical end point. Finite size scaling analysis of the gauge fixed condensate and its cumulants agree with the standard 3D Ising values $\ensuremath{\nu}=0.62997$, $\ensuremath{\beta}/\ensuremath{\nu}=0.518$, $\ensuremath{\gamma}/\ensuremath{\nu}=1.964$ at $\ensuremath{\lambda}=0.00150$. These results are in agreement with previous studies suggesting 3D Ising universality class. The numerical results also indicate that, at the transition point, the gauge fixed condensate vanishes in the infinite volume limit.

Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions

We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions (PD) within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead a weakly first-order transition is identified from both thermal properties and the distribution of the nematic order parameter. Furthermore, based on PD calculations, we obtain exact results for the order parameter distribution and Binder cumulants at the discontinuous melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.

Фазовые переходы в двумерной слабо разбавленной четырехкомпонентной модели Поттса на гексагональной решетке

The Monte Carlo method is used to study phase transitions in a two-dimensional weakly diluted 4-state Potts model on a hexagonal lattice. Systems with linear dimensions L=21÷336 at spin concentrations p=1.00, 0.90 are considered. The use of the fourth-order binder cumulants method and histogram data analysis showed that the introduction of non-magnetic impurities has a stabilizing role in the implementation of the second-order phase transition in the Potts model under study on a hexagonal lattice.

Phase transitions in a two-dimensional weakly diluted 4-state Potts model on a hexagonal lattice

The Monte Carlo method is used to study phase transitions in a two-dimensional weakly diluted 4-state Potts model on a hexagonal lattice. Systems with linear dimensions L=21/336 at spin concentrations p=1.00, 0.90 are considered. The use of the fourth-order binder cumulants method and histogram data analysis showed that the introduction of nonmagnetic impurities has a stabilizing role in the implementation of the second-order phase transition in the Potts model under study on a hexagonal lattice. Keywords: Potts model, Monte Carlo method, thermodynamic parameters, disorder.

Finite-size scaling of the majority-voter model above the upper critical dimension

The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension d = 2 to 7 with periodic boundary conditions. The critical exponents associated to the finite-size scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension d = 4, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For d ≥ 5, the estimates of the exponents are close to the prediction d/2 when taking into account the dangerous irrelevant variable at the Gaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not dc = 6 as claimed in the literature, but dc = 4 like the equilibrium Ising model.

Geometric cumulants associated with adiabatic cycles crossing degeneracy points: Application to finite size scaling of metal-insulator transitions in crystalline electronic systems

In this work we focus on two questions. One, we complement the machinary to calculate geometric phases along adiabatic cycles as follows. The geometric phase is a line integral along an adiabatic cycle, and if the cycle encircles a degeneracy point, the phase becomes non-trivial. If the cycle crosses the degeneracy point the phase diverges. We construct quantities which are well-defined when the path crosses the degeneracy point. We do this by constructing a generalized Bargmann invariant, and noting that it can be interpreted as a cumulant generating function, with the geometric phase being the first cumulant. We show that particular ratios of cumulants remain finite for cycles crossing a set of isolated degeneracy points. The cumulant ratios take the form of the Binder cumulants known from the theory of finite size scaling in statistical mechanics (we name them geometric Binder cumulants). Two, we show that the machinery developed can be applied to perform finite size scaling in the context of the modern theory of polarization. The geometric Binder cumulants are size independent at gap closure points or regions with closed gap (Luttinger liquid). We demonstrate this by model calculations for a one-dimensional topological model, several two-dimensional models, and a one-dimensional correlated model. In the case of two dimensions we analyze to different situations, one in which the Fermi surface is one-dimensional (a line), and two cases in which it is zero dimensional (Dirac points). For the geometric Binder cumulants the gap closure points can be found by one dimensional scaling even in two dimensions. As a technical point we stress that only certain finite difference approximations for the cumulants are applicable, since not all approximation schemes are capable of extracting the size scaling information in the case of a closed gap system.

Ising model on a 2D additive small-world network

In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a spin variable that interacts with the nearest neighbor and has a certain probability p of being additionally connected at random to one of its farther neighbors. The system is in contact with a heat bath at a given temperature T and it is simulated by one-spin flip according to the Metropolis prescription. We have calculated the thermodynamic quantities of the system, such as, the magnetization per spin m, magnetic susceptibility chi, and the reduced fourth-order Binder cumulant U as a function of T for several values of lattice size L and additive probability p. We also have constructed the phase diagram for the equilibrium states of the model in the plane T versus p showing the existence of a continuous transition line between the ferromagnetic F and paramagnetic P phases. Using the finite-size scaling (FSS) theory, we have obtained the critical exponents for the system, where varying the parameter p, we have observed a change in the critical behavior from the regular square lattice Ising model to A-SWN.

The tricritical point of the site-diluted three-dimensional 5-state Potts model

The phase transitions in the three-dimensional standard weakly diluted 5-state Potts model on a simple cubic lattice are examined by computer simulation. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p = 1.0; 0.90; 0.85; 0.8. The value of the tricritical point pt in the phase diagram is found using Binder cumulants and histogram analysis of the data. Magnetic structures corresponding to different temperature regimes in the vicinity of the tricritical point are obtained.

The Behavior of the Three-Dimensional Askin–Teller Model at the Mixed Phase Region by a New Monte Carlo Approach

The new approach of performing Monte Carlo (MC) simulations, which eliminates large oscillations of the values of the thermodynamic quantities computed for a mixed phase region, is demonstrated. The results are presented on the example of the mixed phase region in the 3D Askin–Teller (AT) model, where within a certain range of parameters with equal probabilities there appear two different, but equivalent, ways of ordering two of the three order parameters showing independent behavior. This new approach allowed us to exploit magnetization and internal energy curves, Binder cumulant, Challa- and the Lee-Kosterlitz-like cumulants as well as the internal energy distribution histogram. According to the most effective strategy, in the critical region, we use our recently proposed cluster MC algorithm and the Metropolis algorithm beyond it wherever it is applicable. The existence of two tricritical points and the bifurcation point in this area of the phase diagram is confirmed, and their locations are determined. It is explained that although the system as a whole does not show the presence of latent heat at the boundary of the mixed phase region and the antiferromagnetic phase, it does occur for various order parameters. Specifically, the increase in the energy of the degrees of freedom of one kind is accompanied by an equal decrease in the energy of the degrees of freedom of the other kind.

Short-time dynamics in active systems: the Vicsek model

We study the short-time dynamics (STD) of the Vicsek model (VM) with vector noise. The study of STD has proved to be very useful in the determination of the critical point, critical exponents and spinodal points in equilibrium phase transitions. Here we aim is to test its applicability in active systems. We find that, despite the essential non-equilibrium characteristics of the VM (absence of detailed balance, activity), the STD presents qualitatively the same phenomenology as in equilibrium systems. From the STD one can distinguish whether the transition is continuous or discontinuous (which we have checked also computing the Binder cumulant). When the transition is continuous, one can determine the critical point and the critical exponents.

Monte Carlo studies of the Blume–Capel model on nonregular two- and three-dimensional lattices: phase diagrams, tricriticality, and critical exponents

We perform Monte Carlo simulations, combining both the Wang–Landau and the Metropolis algorithms, to investigate the phase diagrams of the Blume–Capel model on different types of nonregular lattices (Lieb lattice (LL), decorated triangular lattice (DTL), and decorated simple cubic lattice (DSC)). The nonregular character of the lattices induces a double transition (reentrant behavior) in the region of the phase diagram at which the nature of the phase transition changes from first-order to second-order. A physical mechanism underlying this reentrance is proposed. The large-scale Monte Carlo simulations are performed with the finite-size scaling analysis to compute the critical exponents and the critical Binder cumulant for three different values of the anisotropy , showing thus no deviation from the standard Ising universality class in two and three dimensions. We report also the location of the tricritical point to considerable precision: (Δ t /J = 1.3457(1); k B T t /J = 0.309(2)), (Δ t /J = 1.5766(1); k B T t /J = 0.481(2)), and (Δ t /J = 1.5933(1); k B T t /J = 0.569(4)) for LL, DTL, and DSC, respectively.