Frustration - how it can be measured

TL;DR

This paper introduces a misfit parameter to quantify frustration in physical and combinatorial systems, enabling comparison across models and extending to various optimization problems.

Contribution

It proposes a new measure for frustration, applicable to different models and problems, facilitating comparative analysis and broader application.

Findings

Misfit parameter effectively characterizes frustration in spin-glass models.

Allows comparison of different frustrated systems.

Extension to other combinatorial optimization problems demonstrated.

Abstract

A misfit parameter is used to characterize the degree of frustration of ordered and disordered systems. It measures the increase of the ground-state energy due to frustration in comparison with that of a relevant reference state. The misfit parameter is calculated for various spin-glass models. It allows one to compare these models with each other. The extension of this concept to other combinatorial optimization problems with frustration, e.g. p-state Potts glasses, graph-partitioning problems and coloring problems is given.