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Ferroelectrics

Monte carlo simulations on the simple cubic ising lattice with the dipolar and nearest neighbor interactions

Seizo Watarai, Akira Nakanishi

Published Apr 1, 1990• 2 citations
Publisher

Abstract

Monte Carlo simulations are performed on the simple cubic Ising lattice with both the dipolar and the nearest neighbor interactions. Applying the finite size scaling method, cross over effect of critical phenomena, which has been predicted by the renormalization group theory, can be observed from the Monte Carlo data.
DOI
10.1080/00150199008223832

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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.
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This paper addresses the limitation for routine applications of the proposed Monte Carlo method of direct calculation of absolute free energy by sampling of finite-size dependences and discusses new extensions. The need for multistage sampling is removed and the method is now simpler to apply in practice. To exhibit this, the critical free-energy density for the simple-cubic nearest-neighbor ferromagnetic Ising model is studied for a wide range of lattice sizes, up to 32\ifmmode\times\else\texttimes\fi{}32\ifmmode\times\else\texttimes\fi{}32. The finite-size scaling is demonstrated and the scaling amplitude calculated with higher accuracy than before. These results indicate the possibility that very accurate free-energy density and related quantities such as surface free energy, can be routinely obtained for lattice models from Monte Carlo simulations, even at criticality.