Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump

TL;DR

This paper provides numerical evidence that the Kosterlitz-Thouless transition's discontinuous nature can be directly observed through a higher order derivative of the free energy, offering new insights into its universal characteristics.

Contribution

It introduces a novel approach linking the discontinuity of the helicity modulus to a higher order free energy derivative without prior assumptions about the transition's nature.

Findings

Discontinuous helicity modulus at KT transition confirmed

Higher order free energy derivative is intrinsically linked to the transition

Potential universal number associated with the higher order derivative

Abstract

It is numerically shown that the discontinuous character of the helicity modulus of the two-dimensional XY model at the Kosterlitz-Thouless (KT) transition can be directly related to a higher order derivative of the free energy without presuming any {\it a priori} knowledge of the nature of the transition. It is also suggested that this higher order derivative is of intrinsic interest in that it gives an additional characteristics of the KT transition which might be associated with a universal number akin to the universal value of the helicity modulus at the critical temperature.