arXiv:physics/0404030 · Brazilian Journal of Physics

Monte Carlo study of the spin-1 Baxter-Wu model

M. L. M. Costa, J. A. Plascak

Published Jun 1, 2004• 8 citations

Abstract

The two-dimensional spin-1 Baxter-Wu model is studied by using Monte Carlo simulations. The standard single-spin-flip Metropolis algorithm is used to generate the configurations from which the order parameter, specific heat and magnetic susceptibility are measured. The finite-size scaling procedure is employed in order to get the critical behavior. Extensive simulations show that the critical exponents are different from those of the spin-1/2 model suggesting that the spin-1 model is in a different universality class.

DOI: 10.1590/s0103-97332004000300017

Related papers

Monte Carlo study of the Spin-1 Baxter-Wu model in a crystal field

M. L. M. Costa, J. A. Plascak

The two-dimensional Baxter-Wu model with spin-1, in the presence of a crystal field, is studied by using Monte Carlo simulations. The standard single-spin-flip Metropolis algorithm is used to generate the configurations from which the order parameter, specific heat and magnetic susceptibility are measured. Single histogram techniques are used to get the results close to the phase transitions. The finite-size scaling procedure is employed in order to obtain the critical behavior. The simulations have shown that the critical exponents are different from the spin-1/2 case and are crystal field dependent.

Journal of Physics Conference SeriesJan 1, 20165 citations

O modelo de Baxter-WU Spin-1

Maria Lucia de Morais Costa

We have studied the critical, multicritical and first order behavior of the Spin-1 Baxter-Wu model in a crystal field. We have employed the mean field renormalization group approach and extensive Monte Carlo simulations using the single spin flip Metropolis algorithm and hystogram techniques. The global phase diagram is obtained and it is shown that the system belongs to the same universality class as the corresponding spin-1/2 version and presents a multicritical point separating a second order phase transition line from a first order line. The probability distribution of this pentacritical point is also determined.

Dec 12, 20050 citations

Two-dimensional dilute Baxter-Wu model: Transition order and universality

A. R. S. Macêdo, Alexandros Vasilopoulos, M. Akritidis +3 more

We investigate the critical behavior of the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal-field coupling Δ with the goal of determining the universality class of transitions along the second-order part of the transition line as one approaches the putative location of the multicritical point. We employ extensive Monte Carlo simulations using two different methodologies: (i) a study of the zeros of the energy probability distribution, closely related to the Fisher zeros of the partition function, and (ii) the well-established multicanonical approach employed to study the probability distribution of the crystal-field energy. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram supports previous claims that the transition belongs to the universality class of the four-state Potts model. For positive values of Δ, we observe the presence of strong finite-size effects, indicative of crossover effects due to the proximity of the first-order part of the transition line. Finally, we demonstrate how a combination of cluster and heat-bath updates allows one to equilibrate larger systems, and we demonstrate the potential of this approach for resolving the ambiguities observed in the regime of Δ≳0.

arXiv:2304.12379Physical review. EAug 25, 20236 citations

Monte Carlo simulation of phase transitions in a two-dimensional random-bond Potts model

S. Chen, Alan M. Ferrenberg, D. P. Landau

Using the ``multihit'' Swendsen-Wang cluster flipping method, we performed extensive Monte Carlo simulations to investigate the critical behavior of the two-dimensional (2D) eight-state random-bond Potts model. We applied finite-size-scaling techniques to extract the critical exponents for two different sets of bond strengths, from which we concluded that the transition is second order with critical exponents for both sets falling into same universality class, that of a 2D Ising model. A variation of the Lee-Kosterlitz method for determining the order of a phase transition was also applied. The double-peaked structure of the specific heat, which was found in some of the bond configurations, was also studied by simulation on periodic arrangements of strong and weak bonds.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsAug 1, 1995105 citations

Probability distribution of the order parameter

P. H. L. Martins, J. A. Plascak

The probability distribution of the order parameter is analyzed in order to obtain the criticality of magnetic systems. Monte Carlo simulations have been employed by using single spin flip Metropolis algorithm aided by finite-size scaling and histogram reweighting techniques. A method is proposed to obtain this probability distribution even when the transition temperature of the model is unknown. A test is performed on the two-dimensional spin-1/2 and spin-1 Ising model and the results show that the present procedure can be quite efficient and accurate to describe the criticality of the system.

arXiv:cond-mat/0404231Brazilian Journal of PhysicsJun 1, 200416 citations

Critical Behavior Simulation of the Two-Dimensional Ising Model—A Computational Physics Study Based on the Monte Carlo Method

佳钢李

To demonstrate the application of computational physics in modern statistical physics, this paper investigates the critical behavior of a finite-size ferromagnetic system based on the two-dimensional square-lattice Ising model.A nearest-neighbor Ising Hamiltonian is constructed, and periodic boundary conditions are adopted to reduce finite-boundary effects.The Metropolis Monte Carlo algorithm is used to sample spin configurations at different temperatures, while energy, magnetization, specific heat, magnetic susceptibility and Binder cumulant are calculated to describe the transition from an ordered state to a disordered state.The simulation results show that the system exhibits clear long-range order at low temperatures, where the order parameter remains high.As temperature increases, thermal fluctuations become stronger, magnetization decreases rapidly, and the system gradually evolves into a disordered state.The specific heat curve shows a pronounced peak at approximately (T = 2.269), while the susceptibility peak shifts slightly toward the high-temperature side due to finite-size effects and the discrete temperature grid.Overall, the simulated critical region is consistent with the theoretical critical temperature of the two-dimensional square-lattice Ising model.Spin-configuration analysis further reveals enhanced fluctuations and domain reconstruction near the critical region.In addition, a thermalization criterion and an extended sampling test for L = 48 near the critical region are added to examine the influence of finite sampling and equilibration.These results indicate that Monte Carlo simulation of the two-dimensional Ising model can effectively reproduce continuous phase transition, critical fluctuation and finite-size effects, providing a basic computational case for understanding critical phenomena in complex systems and data-driven physical analysis.

Modern PhysicsJan 1, 20260 citations