The Numerical Simulation Study Of Ising Model

Phase transition, is a kind of break phenomena which exits in the nature widely, is a kind of transition process in which substance system changes from one steady state to another, and is an important research area in Physics. The commonest phase transitions are the paramagnetic-ferromagnetic phase transition and the liquid-gas phase transition, etc. Recent years, with the development of computer technology, numerical calculation has become an effective method to research phase transitions and critical phenomena. This paper uses the numerical simulation method to study the phase transition of Ising model, including classical two-dimension Ising model, two-dimension Ising model with next-nearest interaction and Ising model on a small world network.First of all, this paper discusses the numerical simulation method from the view of theory, namely the Monte Carlo method, introducing the detailed balance condition, the important sampling and the Metropolis algorithm. On the basis of this, I analyze the classical two-dimension Ising model using the numerical simulation method and compare the result with the precision result. It shows that the numerical simulation method is very effective.Secondly, I construct the Ising model with next-nearest interaction on the basis of classical Ising model. Similarly, I analyze the phase transition of the model, compare its result with the result of classical two-dimension Ising model, and find that the changing of properties of the system with next-nearest neighbor interaction getting greater exhibits regularity.Finally, I study how complex networks influence Ising model. This is a new research area, and is very wide. This paper mainly studies how the statistical properties of complex networks influence the dynamical process on the networks. This paper constructs a small world network on a one-dimension ring chain and studies the phase transition of the Ising model on the small world network. One-dimension Ising model has no phase transition, but the Ising model on the small world network constructed from the one-dimension ring chain has phase transition. This paper briefly analyzes its phase transition.