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Vestnik of Samara University Natural Science Series

MONTE-CARLO CALCULATIONS OF PHASE TRANSITION TEMPERATURE IN THE ISING MODEL WITH LONG RANGE INTERACTIONS

Alexander Alexandrovich Biryukov, Y.V. Degtyarova

Published Dec 17, 2015• 0 citations
Publisher

Abstract

The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance r as a power law r-d-σ with dimensional d and parameter σ. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of nu- merical simulation the dependence of the phase transition temperature on the parameter σ is found. It is shown that at phase transition temperature decreases with increasing σ.

DOI
10.18287/2541-7525-2015-21-6-161-170

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The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance r as a power law r-d-σ with dimensional d and parameter σ. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of nu- merical simulation the dependence of the phase transition temperature on the parameter σ is found. It is shown that at phase transition temperature decreases with increasing σ.
The article deals with two-dimensional and three-dimensional Ising models with the long-range spin interactions. The intensity of interaction between the spins relies decreasing with distance r as a power law r-d-σ with dimensional d and parameter σ. The research are conducted by Monte-Carlo method with Metropolis algorithm using parallel computing techniques. On the basis of nu- merical simulation the dependence of the phase transition temperature on the parameter σ is found. It is shown that at phase transition temperature decreases with increasing σ.
We simulate the Ising Model with the Monte Carlo method and use the algorithms of Metropolis to update the distribution of spins. We found that, in the specific case of the three-dimensional Ising Model, methods of Metropolis are efficient. Studying the system near the point of phase transition, we observe that the magnetization goes to zero. In our simulations we analyzed the behavior of the magnetization and magnetic susceptibility to verify the phase transition in a paramagnetic to ferromagnetic material. The behavior of the magnetization and of the magnetic susceptibility as a function of the temperature suggest a phase transition around KT/J ≈ 4.5 and was evidenced the problem of finite size of the lattice to work with large lattice.