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

• Published in: arXiv.org 2000-04
• Main Authors: Kitatani, H, Sinada, A
• Format: Article
• Language: English
• Subjects: Ising model; Mathematical models; Order parameters; Parameter modification; Phase transitions; Scaling; Spin glasses; Two dimensional models
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.9908370

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.