Autocorrelation analysis on a 3D Ising model near the phase transition

David Aceituno Chávez

Bernardo Fierro, F. Bachmann, Eugenio Emilio Vogel

L. G. Rizzi, Nelson A. Alves

Artur Falqueto Sonsin, M R Cortes, D.R.M. Nunes +2 more

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.

Dorota Jeziorek-Knioła, Grzegorz Musiał, L. Dębski +2 more

The phase transition line near the Ising point region is studied for the 3D standard AshkinTeller model on a cubic lattice.This model with a multicomponent order parameter is one of the important reference points in statistical physics since it shows an interesting and complicated phase diagram.The main motivation for our study was nonuniversal behavior suggested for this line.The large-scale Monte Carlo simulations using the Binder and Challa like cumulants are performed.Accurate analysis to exclude the latent heat inherence is applied.Specic behavior of the Challa like cumulants is discovered and its interpretation is proposed.The paper is closed with preliminary conclusions concerning the continuous but non-Ising character of these phase transitions in the lower part of the mixed phase region and the possiblity of the rst order on the line connecting it to the Ising point.

Valeriy A Ryabov