The Ising Spin Glass in dimension four

Abstract

The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein {\it et al.} (1991). The simulations include standard finite size scaling measurements, thermodynamic limit regime measurements, and analyses which provide estimates of critical exponents without any consideration of the critical temperature. The higher order HTSE series for the bimodal model provide accurate estimates of the critical temperature and critical exponents. These estimates are independent of and fully consistent with the simulation values. Comparisons between ISG models in dimension four show that the critical exponents and the critical constants for dimensionless observables depend on the form of the interaction distribution of the model.

10 pages, 15 figures

References in corpus (7)

• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• The critical behavior of three-dimensional Ising spin glass models
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Cited by in corpus (2)

• The bimodal Ising spin glass in dimension two : the anomalous dimension $\eta$
• Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant