Soft annealing: A new approach to difficult computational problems

Abstract

I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system with the hard constraints replaced by soft constraints. I illustrate the method in the case of the ferromagnetic Ising model and in the case the three dimensional spin-glass model. I show in both the ferromagnetic Ising and the spin-glass model that the phases of the soft problem have the same properties with the phases of the original model and that the softened model belongs to the same universality class as the original one. I show that correlation times are much shorter in the larger soft constrained system and that it is computationally advantageous to study it instead of the original system. This method is quite general and can be applied to other systems.