Finite Size Analysis of the One-dimensional $q = \infty$ Clock Model

TL;DR

This paper investigates the finite size scaling behavior of the one-dimensional $q=\

Contribution

It provides a detailed analysis of finite size effects in the $q ightarrow \\infty$ clock model, revealing non-universal corrections and behaviors akin to second order phase transitions.

Findings

Specific heat and cumulants match first order transition predictions

Leading correction to extremal points is non-universal

Mass gap corrections behave like second order transitions

Abstract

We analyze the finite size scaling of the $q$-state clock model in the $q \rightarrow \infty$ limit. The behaviors of the specific heat, Binder-Landau and U4 cumulants agree with the Borgs-Koteck\'y ans\"atz for first order phase transitions. However, we find that the leading correction to the position of the extremal points of these quantities is not universal. On the other hand, the finite size corrections to the mass gap behave like for second order phase transitions. In particular, the curves corresponding to different size approximations do not cross in the vicinity of the transition points. The feature is associated to the existence of a divergent correlation length and holds for a wider class of models.