Frustrated Systems: Ground State Properties via Combinatorial Optimization

TL;DR

This paper explores how combinatorial optimization techniques can be applied to compute ground state properties of various frustrated and disordered physical systems, providing both theoretical insights and algorithmic approaches.

Contribution

It introduces combinatorial optimization methods to analyze ground states of frustrated systems, highlighting algorithms like network flows and matching for complex disordered models.

Findings

Application of network flow algorithms to spin systems

Analysis of disordered models using combinatorial optimization

Comparison of algorithmic approaches for ground state calculations

Abstract

An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising model, the diluted antiferromagnet in an external field, the spin glass problem, the solid-on-solid model with a disordered substrate and other convex cost flow problems occurring in superconducting flux line lattices and traffic flow networks. On the algorithmic side we present a concise introduction to a number of elementary algorithms in combinatorial optimization, in particular network flows: the shortest path algorithm, the maximum-flow algorithms and minimum-cost-flow algorithms. We present a short glance at the minimum weighted matching and branch-and-cut algorithms.