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

Abstract

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 $T_{\mathrm{c}}$ is strongly affected by the corrections to scaling within the present data ($L\le 23$). Thus, there still remains the possibility that $T_{\mathrm{c}}=0$, contrary to the recent results which suggest the existence of a finite-temperature spin-glass phase transition.

10 pages,8 figures: final version to appear in J. Phys. A

References in corpus (3)

• Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions
• Defect Energy with Conjugate Boundary Conditions in Spin Glass Models in Two Dimensions
• Low Temperature Phase of Asymmetric Spin Glass Model in Two Dimensions

Cited by in corpus (2)

• An exact algorithm for spin correlation functions of the two dimensional +/-J Ising spin glass in the ground state
• The Compressible Ising Spin Glass: Simulation Results