Honeycomb lattice solvable models

TL;DR

This paper introduces exactly solvable models on the honeycomb lattice by integrating square lattice models into hexagon faces, revealing their critical behavior and phase transitions, with potential extensions to Z-invariant models.

Contribution

It presents a novel construction of honeycomb lattice solvable models from square lattice models, including analysis of their critical properties and phase transitions.

Findings

Transfer matrices commute with different spectral parameters.

Finite-size scaling relates honeycomb models to square lattice models.

Detailed phase transition analysis for two specific models.

Abstract

We construct solvable models on the honeycomb lattice by combining three faces of the square lattice solvable models into a hexagon face. These models contain two independent, anisotropy controlling, spectral parameters and their transfer matrices with different spectral parameters commute with each other. At the critical point, the finite-size scaling of the transfer matrix spectrum for the honeycomb lattice models is written in terms of the quantities obtained from the finite-size scaling of the square lattice solvable models. We study in detail the phase transition properties of two models based on the interacting hard square model and the magnetic hard square model, respectively. The models, in general, can be extended to the IRF version of the Z-invariant models of Baxter.