Ground states of 2d +-J Ising spin glasses via stationary Fokker-Planck sampling

TL;DR

This paper evaluates the stationary Fokker-Planck sampling method for finding ground states in 2D +-J Ising spin glasses, highlighting its performance, optimal parameters, and limitations compared to other methods.

Contribution

It introduces and tests a stationary Fokker-Planck sampling approach for spin glass ground state optimization, analyzing its effectiveness and limitations.

Findings

Identifies an optimal diffusion parameter D for the algorithm.

Shows the algorithm's decreasing success with increasing lattice size.

Finds the method is less effective than parallel tempering for larger systems.

Abstract

We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a linear second order differential equation that depends on a diffusion-like parameter D. We apply it to the problem of finding ground states of 2d Ising spin glasses for the +-J-Model. We consider square lattices with side length up to L=24 with two different types of boundary conditions and compare the results to those obtained by exact methods. A particular value of D is found that yields an optimal performance of the algorithm. We compare this optimal value of D to a percolation transition, which occurs when studying the connected clusters of spins flipped by the algorithm. Nevertheless, even for moderate lattice sizes, the algorithm has more and more problems to find the exact ground states. This means that the approach, at least in its standard form, seems to be inferior to other approaches like parallel tempering.