# On the origin of Phase Transitions in the absence of Symmetry-Breaking

## TL;DR

This paper explores a three-dimensional lattice gauge model that exhibits a first-order phase transition without symmetry-breaking, using topological and configurational entropy analyses to understand the transition's nature.

## Contribution

It introduces a Hamiltonian model based on a continuum duality transformation of the 3D Ising model that undergoes a non-symmetry-breaking phase transition and analyzes it through topological and entropy-based methods.

## Key findings

- The model exhibits a first-order phase transition without symmetry-breaking.
- The phase transition is characterized by an Ehrenfest-like classification applied to configurational entropy.
- Divergent behavior of the third derivative of entropy is linked to topological changes in configuration space.

## Abstract

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimension. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model. The system so obtained undergoes a thermodynamic phase transition in the absence of symmetry-breaking. Besides the well known use of quantities like the Wilson loop we show how else the phase transition in such a kind of models can be detected. It is found that the first order phase transition undergone by this model is characterised according to an Ehrenfest-like classification of phase transitions applied to the configurational entropy. On the basis of the topological theory of phase transitions, it is discussed why the seemingly divergent behaviour of the third derivative of configurational entropy can be considered as the "shadow" of some suitable topological transition of certain submanifolds of configuration space.