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arXiv:cond-mat/0701039

Comment on ``Phase transitions in a square Ising model with exchange and dipole interactions'' by E. Rastelli, S. Regina and A. Tassi

Sergio Alejandro Cannas, Mateus Fontana Michelon, Mateus Fontana Michelon, Francisco A. Tamarit

Published Jan 2, 2007• 0 citations
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Abstract

We discuss numerical results presented in a recent ppublication about the critical properties of a two dimensional Ising model with exchange and dipolar interactions.
DOI
10.48550/arxiv.cond-mat/0701039

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Monte Carlo simulations are performed on the square lattice Ising system with both the nearest neighbor and the two-dimensional dipolar interactions in order to investigate the critical property of ferromagnetic phase transitions in this 2-dimensional system. Applying the finite size scaling theory to Monte Carlo data just near the transition point, the critical indices of this dipolar system are calculated and α=0.31±0.04, β =0.20±0.02, γ=1.08±0.20 and ν=0.72±0.10 are obtained. However, in the temperature region considerably far from the transition point, different values of α, β and γ seem to be adequate, which are rather close to those of the rigorous result of the 2-dimensional Ising model.
In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width nnn (hn)({h}_{n})(hn​) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants $\ensuremath{\delta}$. The obtained results indicate that the h1{h}_{1}h1​-TL phase transition line is continuous up to $\ensuremath{\delta}=1.2585$, while for the h2{h}_{2}h2​-TL line a weak first-order character is found in the interval $1.2585\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}1.36$ and becomes continuous for $1.37\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}1.9$. This result suggests the existence of a tricritical point close to $\ensuremath{\delta}=1.37$. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on $\ensuremath{\delta}$ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the ${h}_{1}\ensuremath{-}{h}_{2}$ line, i.e., at $\ensuremath{\delta}=1.2585$, the critical phase corresponding to the ${h}_{1}\ensuremath{-}\mathrm{TL}$ transition coexists with the h2{h}_{2}h2​ phase.