Cluster Dynamics for Randomly Frustrated Systems with Finite Connectivity

TL;DR

This paper compares cluster algorithms and Metropolis dynamics in finite connectivity spin glass systems, showing that cluster algorithms achieve lower energy states and can reach ground states analytically predicted under replica symmetry.

Contribution

It introduces a detailed analysis of cluster dynamics in finite connectivity spin glasses, demonstrating their effectiveness over Metropolis methods and providing analytical ground state calculations.

Findings

Cluster algorithms achieve lower saturated energies than Metropolis.

The energy gap is robust across different annealing schedules.

Analytical ground state energies are obtained under replica symmetry.

Abstract

In simulations of some infinite range spin glass systems with finite connectivity, it is found that for any resonable computational time, the saturatedenergy per spin that is achieved by a cluster algorithm is lowered in comparison to that achieved by Metropolis dynamics.The gap between the average energies obtained from these two dynamics is robust with respect to variations of the annealing schedule. For some probability distribution of the interactions the ground state energy is calculated analytically within the replica symmetry assumptionand is found to be saturated by a cluster algorithm.