Phase Transition of XY Model in Heptagonal Lattice

TL;DR

This paper explores the phase transition behavior of the XY model on a heptagonal lattice with negative curvature, revealing a zero-temperature transition driven by strong fluctuations, contrasting with finite-temperature transitions in other structures.

Contribution

It provides the first numerical analysis of the XY model on a negatively curved heptagonal lattice, highlighting unique phase transition properties compared to flat and small-world networks.

Findings

Heptagonal lattice exhibits a zero-temperature phase transition.

Strong spinwave fluctuations suppress finite-temperature transition.

Contrast with mean-field behavior in small-world networks.

Abstract

We numerically investigate the nature of the phase transition of the XY model in the heptagonal lattice with the negative curvature, in comparison to other interaction structures such as a flat two-dimensional (2D) square lattice and a small-world network. Although the heptagonal lattice has a very short characteristic path length like the small-world network structure, it is revealed via calculation of the Binder's cumulant that the former exhibits a zero-temperature phase transition while the latter has the finite-temperature transition of the mean-field nature. Through the computation of the vortex density as well as the correlation function in the low-temperature approximation, we show that the absence of the phase transition originates from the strong spinwave-type fluctuation, which is discussed in relation to the usual 2D XY model.