Exact Solution of a Three-Dimensional Dimer System

TL;DR

This paper provides an exact analytical solution for a three-dimensional dimer system by relating it to two-dimensional vertex models, enabling detailed analysis of phase transitions in 3D lattice models.

Contribution

It introduces an exact solution method for a 3D dimer system using transfer matrix techniques linked to 2D vertex models, which is a novel approach.

Findings

Eigenvalues and eigenvectors related to 2D vertex models

Analysis of phase transitions in 3D dimer systems

Exact transfer matrix solution for layered lattice models

Abstract

We consider a three-dimensional lattice model consisting of layers of vertex models coupled with interlayer interactions. For a particular non-trivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. The result is applied to analyze the phase transitions in a realistic three-dimensional dimer system.