Thermodynamics of the two-dimensional XY model from functional renormalization

TL;DR

This paper applies nonperturbative renormalization-group methods to analyze the thermodynamics of the 2D XY model, accurately capturing the specific heat behavior and highlighting limitations of simplified truncations.

Contribution

It provides a detailed nonperturbative RG analysis of the 2D XY model's thermodynamics, emphasizing the importance of infinite interaction vertices for accurate results.

Findings

Results agree well with Monte Carlo simulations.

Simplified $$-type truncations are insufficient in the high-temperature phase.

Correct specific heat profiles require accounting for infinite interaction vertices.

Abstract

We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $\phi^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.