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Journal of Physics Conference Series

Monte Carlos studies of critical and dynamic phenomena in mixed bond Ising model

J.B. Santos-Filho, N. O. Moreno, Douglas F. de Albuquerque

Published Nov 1, 2010• 2 citations
Publisher

Abstract

The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Metropolis and Wolff algorithm with histogram technique and finite size scaling theory to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters.

DOI
10.1088/1742-6596/249/1/012038

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The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Metropolis and Wolff algorithm with histogram technique and finite size scaling theory to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters.
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Cluster algorithms of Wolff and Glauber to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters
The critical properties of a random mixed-bond Ising model on a cubic lattice are studied so much  numerically with analytically. Analytical studies on Mixed-bond Ising model through renormalization  group technique predict the existence of reentrant magnetism in certain range of values of the  competition parameter α. This phenomenon typically found in systems that present spin-glass phase. In  this work, did we use the algorithm cluster of Wolff to simulate the dynamics of the system. Using the  technique of the Histogram obtains the thermodynamic amounts of interest and based on the theory finite  size scaling found the critical temperatures, the phase diagrams and the critical exponents of the model. Our results were compared with those obtained using a new technique in effective field theory which  employs similar probability distribution within the framework of two-site clusters.
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied bothnumerically and analytically. Analytical studies on Mixed-bond Ising model by using renormalizationgroup technique predict the existence of reentrant magnetism in a certain range of values of thecompetition parameter α. This phenomenon typically is found in systems presenting spin glass phase, forinstance EupSr1-p. We seek the existence of the reentrance by means of Monte Carlo simulations. In thiswork, we use the Cluster algorithms de Wolff to simulate the dynamics of the system. We obtained thethermodynamic quantities such as magnetization and susceptibility. Critical temperatures were estimatedof the maximum of the susceptibility and with these values we made the phase diagram Tc versus p fordifferent α values. Our results were compared with those obtained using a new technique in effective fieldtheory which employs similar probability distribution within the framework of two-site clusters.
In the present work, we present an extensive Monte Carlo simulation study on the dynamical properties of the two-dimensional random-bond Ising model. The correlation time τ of the Swendsen-Wang and Wolff cluster algorithms is calculated at the critical point. The dynamic critical exponent z of both algorithms is also measured by using the numerical data for several lattice sizes up to L=512. It is found for both algorithms that the autocorrelation time decreases considerably and the critical slowing-down effect reduces upon the introduction of bond disorder. Additionally, simulations with the Metropolis algorithm are performed, and the critical slowing-down effect is observed to be more pronounced in the presence of disorder, confirming the previous findings in the literature. Moreover, the existence of the non-self-averaging property of the model is demonstrated by calculating the scaled form of the standard deviation of autocorrelation times. Finally, the critical exponent ratio of the magnetic susceptibility is estimated by using the average cluster size of the Wolff algorithm.
This study presents a comprehensive Monte Carlo simulation of the two-dimensional (2-D) Ising model using the Metropolis algorithm to investigate critical phenomena and thermodynamic behavior in spin-lattice systems. The model, implemented in MATLAB with periodic boundary conditions, explores equilibrium properties such as magnetization, internal energy, specific heat, and susceptibility across a range of temperatures. By employing various initial spin configurations—ordered and random—the simulations demonstrate the system's ergodicity and convergence to thermal equilibrium. Key results include a sharp decline in magnetization and a pronounced peak in specific heat near the critical temperature, consistent with second-order phase transition behavior. The simulation captures microscopic domain evolution, highlighting the transition from ferromagnetic to paramagnetic phases as thermal fluctuations increase. The study further evaluates algorithmic efficiency, discusses the impact of lattice size on statistical accuracy, and proposes improvements using advanced cluster algorithms and parallel computing frameworks. The findings validate theoretical predictions from Onsager's solution and underscore the versatility of Monte Carlo techniques in modeling collective behavior in magnetic systems. The simulation framework offers a robust foundation for analyzing critical dynamics and extends its relevance to broader applications in material science, computational physics, and complex systems modeling.
We apply numerical simulations to study the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio Γ+/Γ−Γ^+/Γ^-Γ+/Γ− for the magnetic susceptibility critical amplitudes. Our estimate Γ+/Γ−=1.67±0.15Γ^+/Γ^- = 1.67 \pm 0.15Γ+/Γ−=1.67±0.15 is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.