Constrained Annealing for Spin Glasses

The quenched free energy of spin glasses can be estimated by means of annealed averages where the frustration or other self-averaging variables of disorder are constrained to their average value. We discuss the case of d-dimensional Ising models with random nearest neighbour coupling, and for ± J spin glasses we introduce a new method to obtain constrained annealed averages without recurring to Lagrange multipliers. It requires to perform quenched averages either on small volumes in an analytic way, or on finite size strips via products of random transfer matrices. We thus give a sequence of converging lower bounds for the quenched free energy of 2d spin glasses