A Soluble Free-Fermion Model in d Dimensions

TL;DR

This paper introduces a d-dimensional vertex model with free-fermion conditions, solvable via a Pfaffian approach, and analyzes its critical behavior and phase transitions.

Contribution

It presents a new solvable vertex model in arbitrary dimensions using free-fermion conditions and Pfaffian techniques, extending previous two-dimensional models.

Findings

Model is soluble under free-fermion condition

Critical point and singular behavior of free energy determined

Mapping to dimer problem enables exact solution

Abstract

We consider a vertex model in d dimensions characterized by lines which run in a preferred direction. We show that this vertex model is soluble if the weights of vertices with intersecting lines are given by a free-fermion condition, and that a fugacity -1 is associated to each loop of lines. The solution is obtained by mapping the model into a dimer problem and by evaluating a Pfaffian. We also determine the critical point and the singular behavior of the free energy.