CAM Analysis of Dimensionality Crossover

Layered square-lattice ferromagnetic Ising models (∞×∞×n lattices) are studied by the Monte Carlo simulation for n=3 to 9. The results show the dimensionality crossover from the two-dimensional square lattice Ising model to the three-dimensional simple cubic Ising model. The shift exponent λ is estimated to be λ=1.64, which is consistent with the genral expectation that λ=1/ν_. Furthermore, CAM analysis is performed to evaluate the critical exponent γ of the three-dimensional simple cubic ferromagnetic Ising model, which shows that γ=1.21(4). The present analysis is also applicable to the study of the phase transition of quantum spin systems

A New Method to Calculate the Spin-Glass Order Parameter of the Two-Dimensional +/-J Ising Model

A new method to numerically calculate the $n$th moment of the spin overlap of the two-dimensional $\pm J$ Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the $n$th moment of the spin overlap can be calculated as a simple average of the $n$th moment of the total spins with a modified bond probability distribution. The values of the Binder parameter etc have been extensively calculated with the linear size, $L$, up to L=23. The accuracy of the calculations in the present method is similar to that in the conventional transfer matrix method with about $10^{5}$ bond samples. The simple scaling plots of the Binder parameter and the spin-glass susceptibility indicate the existence of a finite-temperature spin-glass phase transition. We find, however, that the estimation of $T_{\rm c}$ is strongly affected by the corrections to scaling within the present data ($L\leq 23$). Thus, there still remains the possibility that $T_{\rm c}=0$, contrary to the recent results which suggest the existence of a finite-temperature spin-glass phase transition.Comment: 10 pages,8 figures: final version to appear in J. Phys.