Graphical proof of Ginibre's inequality

TL;DR

This paper presents a new combinatorial proof of Ginibre's inequality for XY models using multigraph representations and a novel bijection, offering a fresh perspective on this mathematical inequality.

Contribution

It introduces a combinatorial proof leveraging multigraph representations and a new bijection, advancing the understanding of Ginibre's inequality in XY models.

Findings

Provides a new combinatorial proof of Ginibre's inequality

Utilizes multigraph representations and a novel bijection

Offers insights into the structure of XY models

Abstract

In this short note, we will give a new combinatorial proof of Ginibre's inequality for XY models. Our proof is based on multigraph representations introduced by van Engelenburg-Lis (2023) and a new combinatorial bijection.