Domain-wall renormalization-group study of the three-dimensional random Ising model at finite temperature

The three-dimensional random Ising model with a Gaussian distribution of nearest-neighbor interactions is studied for the pure spin-glass case where the average interaction vanishes. The distribution of domain-wall free energies at finite temperature is calculated with the use of the Metropolis Monte Carlo algorithm for finite lattices. A renormalization-group transformation is set up which preserves the domain-wall free-energy distribution when the lattice parameter is changed. The spin-glass transition temperature is found to be $T_g$=(1.0±0.2)J̃ where J̃ is the variance of the Gaussian interaction distribution. The thermal exponent is ν=1.8±0.5 and the heat-capacity exponent is α=-3.4±1.5. The heat capacity exhibits a rounded peak at higher temperatures.