Soft annealing: A new approach to difficult computational problems

TL;DR

This paper introduces a soft annealing method that replaces hard constraints with soft ones in large systems, enabling more efficient simulation of complex models like the Ising and spin-glass models while preserving their critical properties.

Contribution

The paper presents a novel soft annealing approach that simplifies the simulation of difficult problems by replacing hard constraints, maintaining the original system's universality class and reducing correlation times.

Findings

Softened models share the same phase properties as original models.

Correlation times are significantly shorter in the soft constrained systems.

The method is broadly applicable to various complex systems.

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 that in both models the phases of the soft problem have the same properties as 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 many other systems.