Phase Diagram and Critical Exponents of the ±J Ising Model in Finite Dimensions by Monte Carlo Renormalization Group

We have performed large-scale numerical simulations for the ±J Ising model on the simple cubic and the square lattices with asymmetric weight of ferromagnetic and antiferromagnetic bonds. The Monte Carlo renormalization group method is used to estimate T_c, γv, β/v and v at various points along the phase boundary between ferromagnetic and paramagnetic phases including the tricritical point. The obtained values of T_c and the resulting phase diagrams of the simple cubic and the square lattices are much more accurate than those estimated so far. In the simple cubic lattice, we find evidence for the possibility that universality of the ferromagnetic critical exponents holds along the critical line except at the tricritical point, while weak universality holds even at the tricritical point. Weak universality seems to hold also in the square lattice.