The Ising Spin Glass in dimension four

• We present numerical simulations on Ising spin glass models in dimension 4.
• Finite size and thermodynamic limit regime measurements are analyzed.
• The bimodal and Gaussian interaction model critical exponents are different.
• We conclude that these two models are not in the same universality class.

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.