Thermodynamics of the two-dimensional XY model from functional renormalization

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 ${\varphi }^4$-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.

8 pages, 4 figures

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• Universal behavior of coupled order parameters below three dimensions
• Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization
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• Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes