Loop Model with Generalized Fugacity in Three Dimensions

TL;DR

This paper introduces a 3D loop model with a novel global shape-dependent fugacity, demonstrating that a transfer matrix approach remains feasible despite non-locality, and provides numerical entropy estimates.

Contribution

It presents a new 3D loop model with a global shape-dependent fugacity and constructs a transfer matrix despite non-local interactions.

Findings

Transfer matrix can be constructed in 3D with non-local fugacity.

Numerical site entropy estimates in the fully packed limit.

Model extends understanding of non-local interactions in lattice models.

Abstract

A statistical model of loops on the three-dimensional lattice is proposed and is investigated. It is O(n)-type but has loop fugacity that depends on global three-dimensional shapes of loops in a particular fashion. It is shown that, despite this non-locality and the dimensionality, a layer-to-layer transfer matrix can be constructed as a product of local vertex weights for infinitely many points in the parameter space. Using this transfer matrix, the site entropy is estimated numerically in the fully packed limit.