Discontinuous Spontaneous-Symmetry-Breaking in the Microcanonical Ensemble

Hai-Jun Zhou

Published 2019-01-01Version 1

Spontaneous-symmetry-breaking (SSB) is a macroscopic collective phenomenon occurring at phase transitions. Deep understanding of SSB in the canonical statistical ensemble has been achieved in the literature, but SSB in the microcanonical ensemble (with energy being the control parameter) remains largely unexplored. Here we study microcanonical SSB on the paradigmatic Q-state Potts model. For any Q>2, the Bethe-Peierls mean field theory predicts the existence of a discontinuous phase transition in regular random graphs at certain critical energy level, with a jump in the density of the dominant color and in the microcanonical temperature. This discontinuous SSB is the result of entropy competitions at a fixed energy density between the disordered symmetric phase and the microcanonical polarized phase. We confirm by microcanonical Monte Carlo simulations that such a discontinuous SSB also occurs in finite-dimensional lattices. Our work calls for more future theoretical and experimental efforts on microcanonical spontaneous-symmetry-breaking.