Evolving numerical enzymes: Accelerating relaxation in the Frenkel-Kontorova model

Abstract

We have investigated the finite-temperature behavior of the Frenkel-Kontorova model, and have found it unable to reach the ground state when cooled at a finite rate, freezing instead into some metastable configuration. The correlation length of the final state grows as the logarithm of the logarithm of the cooling time. By adding ‘‘numerical enzymes,’’ or long-range Monte Carlo moves which precisely eliminate certain barriers to relaxation, we can equilibrate to significantly lower temperatures. Our numerical method for developing these enzymes is motivated by Darwinian evolution.