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

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 energies at zero temperature is calculated using a Monte Carlo-quench algorithm to find the ground-state energy for finite lattices. A renormalization-group transformation is set up which preserves the domain-wall energy distribution when the lattice parameter is changed. In the strong-coupling regime (zero temperature) the model iterates toward strong coupling and therefore exhibits a spin-glass phase transition at nonzero temperature. The thermal exponent is $\nu =3.0\mathrm{}\pm 1.0$ and the heat capacity exponent is $\alpha =-7\mathrm{}\pm 3$.