Graph's Topology and Free Energy of a Spin Model on the Graph

TL;DR

This paper establishes a relationship between graph topology and the free energy of spin systems, providing a method to compare free energies based on topology alone, with applications to lattice defects and protein design.

Contribution

It introduces a novel method to separate topological and energetic contributions to free energy, enabling qualitative and quantitative comparisons across different graph systems.

Findings

Topology suffices for qualitative free energy comparison at high temperature.

The method explains stability differences in lattice defects.

Closed-form linear contributions predict protein sequence space free energy.

Abstract

In this work we show that there is a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and enthalpic contributions to the free energy, and find that considering the topology is sufficient to qualitatively compare the free energies of different graph systems at high temperature, even when the energetics are not fully known. This method was applied to the metal lattice system with defects, and we found that it partially explains why point defects are more stable than high-dimensional defects. Given the energetics, we can even quantitatively compare free energies of different graph structures via a closed form of linear graph contributions. The closed form is applied to predict the sequence space free energy of lattice proteins, which is a key factor determining the designability of a protein structure.