Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models

TL;DR

This paper provides exact solutions for two complex three-dimensional lattice models involving layered dimers and domain walls, revealing their phase diagrams and transition behaviors through Bethe ansatz analysis.

Contribution

It introduces a novel exact solution for layered lattice models with interlayer interactions by mapping them to a 5-vertex model and applying Bethe ansatz methods.

Findings

Exact free energy expressions derived

Phase diagrams mapped out

Nature of phase transitions identified

Abstract

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.