An exact solution for random mixtures ${\mathit{A}}_{\mathit{x}}$${\mathit{B}}_{1\mathrm{-}\mathit{x}}$ of an Ising model is presented. The solution is obtained in the mean-field version of the model and exhibits a spin-glass phase transition. The explicit dependence of the critical temperature ${\mathit{T}}_{\mathit{c}}$ on the exchange integrals ${\mathit{J}}_{\mathit{A}\mathit{A}}$>0, ${\mathit{J}}_{\mathit{B}\mathit{B}}$>0, ${\mathit{J}}_{\mathit{A}\mathit{B}}$<0, and concentration x, are found. The results are in good agreement with the previous Monte Carlo simulation.

• Received 27 May 1992

DOI:https://doi.org/10.1103/PhysRevB.46.14563