# Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking

## TL;DR

This paper reveals that in the random-graph Potts model, spontaneous symmetry breaking occurs discontinuously due to a kinked entropy function, contrasting with previous continuous transition predictions, and is confirmed through simulations.

## Contribution

It demonstrates that microcanonical SSB can be discontinuous in random graphs due to a kinked entropy, challenging mean field theory expectations.

## Key findings

- Entropy is kinked as a function of energy.
- Discontinuous phase transition with jumps in order parameter and temperature.
- Confirmation via Monte Carlo simulations and finite-size lattice systems.

## Abstract

Spontaneous symmetry breaking (SSB) in statistical physics is a macroscopic collective phenomenon. For the paradigmatic Q-state Potts model it means a transition from the disordered color-symmetric phase to an ordered phase in which one color dominates. Existing mean field theories imply that SSB in the microcanonical statistical ensemble (with energy being the control parameter) should be a continuous process. Here we study microcanonical SSB on the random-graph Potts model, and discover that the entropy is a kinked function of energy. This kink leads to a discontinuous phase transition at certain energy density value, characterized by a jump in the density of the dominant color and a jump in the microcanonical temperature. This discontinuous SSB in random graphs is confirmed by microcanonical Monte Carlo simulations, and it is also observed in bond-diluted finite-size lattice systems.