Soft Annealing: A New Approach to Difficult Computational Problems

I propose a new method to study computationally difficult problems. Iconsider a new system, larger than the one I want to simulate. The originalsystem is recovered by imposing constraints on the large system. I simulate thelarge system with the hard constraints replaced by soft constraints. Iillustrate the method in the case of the ferromagnetic Ising model and in thecase the three dimensional spin-glass model. I show that in both models thephases of the soft problem have the same properties as the phases of theoriginal model and that the softened model belongs to the same universalityclass as the original one. I show that correlation times are much shorter inthe larger soft constrained system and that it is computationally advantageousto study it instead of the original system. This method is quite general andcan be applied to many other systems