The Berezinskii Kosterlitz Thouless phase transition is of second-order in the microcanonical ensemble

TL;DR

This paper demonstrates that the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the 2D XY model is of second order in the microcanonical ensemble, contrasting with its infinite-order nature in the canonical ensemble, highlighting ensemble inequivalence.

Contribution

The study reveals that the BKT transition is second order in the microcanonical ensemble, providing new insights into ensemble inequivalence for systems with BKT transitions.

Findings

BKT transition is second order in the microcanonical ensemble

Ensemble inequivalence observed in BKT phase transitions

Broad applicability to systems with BKT transitions

Abstract

A paradigmatic example of a phase transition taking place in the absence of symmetry-breaking is provided by the Berezinkii-Kosterlitz-Thouless (BKT) transition in the two-dimensional XY model. In the framework of canonical ensemble, this phase transition is defined as an infinite-order one. To the contrary, by tackling the transitional behavior of the two dimensional XY model in the microcanonical ensemble, we show that the BKT phase transition is of second order. This provides a new example of statistical ensemble inequivalence that could apply to a broad class of systems undergoing BKT phase transitions.