Topological aspects of geometrical signatures of phase transitions

TL;DR

This paper investigates the geometric properties of configuration space submanifolds in classical lattice phi^4 models, finding behaviors linked to phase transitions in two dimensions, supporting a topological conjecture about phase transition mechanisms.

Contribution

It provides numerical evidence connecting topological changes in configuration space to phase transitions in classical lattice models.

Findings

Geometric quantities change behavior at phase transition points in 2D models

Supports the topological conjecture relating topology change to phase transitions

Findings are specific to two-dimensional cases with phase transitions

Abstract

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart of a phase transition.