On the nonextensivity of the long range X-Y model

TL;DR

This paper provides analytical and numerical evidence that the long-range X-Y model exhibits extensive internal energy proportional to system size, challenging the expectation of nonextensivity in such models.

Contribution

It demonstrates that the long-range X-Y model's internal energy remains extensive regardless of interaction range, supported by both analytical and numerical analysis.

Findings

Internal energy is proportional to system size N for all interaction ranges.

Analytical and numerical methods confirm the extensivity of the model.

Challenges the assumption that long-range interactions necessarily lead to nonextensivity.

Abstract

It will be given analytical and numerical evidence supporting that the X-Y model yields an extensive, i.e. proportional to the number of degrees of freedom N, internal energy U for any value of the interaction range.