The Ising Spin Glass in dimension four
Résumé
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 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.