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Journal of Xuzhou Normal University

Dynamic Simulation of Ising Model

Tao Yu

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

By use of the Monte Carlo method, a study is made on the square lattices Ising model for different boundary conditions. Combined with the finite size scalar theory, the relevant transition temperatures are obtained and the dynamic processes of the square lattices Ising model in different boundary conditions near the critical point are observed simulatedly. It shows that the phase transition temperatures of the finite Ising systems in different boundary conditions are different, and the speeds getting equilibrium of the systems are different as well, but the difference vanishes at the dynamic limit.

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By use of the Monte Carlo method, a study is made on the square lattices Ising model for different boundary conditions. Combined with the finite size scalar theory, the relevant transition temperatures are obtained and the dynamic processes of the square lattices Ising model in different boundary conditions near the critical point are observed simulatedly. It shows that the phase transition temperatures of the finite Ising systems in different boundary conditions are different, and the speeds getting equilibrium of the systems are different as well, but the difference vanishes at the dynamic limit.
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The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.
We explore the critical properties of the recently discovered finite-time dynamical phase transition in the nonequilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the relaxation dynamics and it occurs at a sharp critical time. While previous works have focused either on mean-field interactions or on investigating the critical time, we analyze the critical fluctuations at the phase transition in the nearest-neighbor Ising model on a square lattice using Monte Carlo simulations. By means of a finite-size scaling analysis, we extract the critical exponents for the transition. In two spatial dimensions, we find that the exponents are consistent with those of the two-dimensional Ising universality class when the system is initially in the vicinity of the critical point. For initial temperatures below the critical one, however, the critical exponents differ from the Ising-exponents, indicating a distinct dynamical critical phenomenon.
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