Monomer-Dimer Mixture on a Honeycomb Lattice

TL;DR

This paper investigates a monomer-dimer mixture on a honeycomb lattice as a model for spin ice in a magnetic field, using theoretical models and numerical methods to analyze phase transitions and fixed points.

Contribution

It combines dual sine-Gordon and Potts lattice gas theories to construct a comprehensive phase diagram for the system.

Findings

Identification of stable and unstable fixed points in the phase diagram.

Numerical transfer-matrix calculations support theoretical predictions.

Construction of a renormalization-group flow diagram for the model.

Abstract

We study a monomer-dimer mixture defined on a honeycomb lattice as a toy model for the spin ice system in a magnetic field. In a low-doping region of monomers, the effective description of this system is given by the dual sine-Gordon model. In intermediate- and strong-doping regions, the Potts lattice gas theory can be employed. Synthesizing these results, we construct a renormalization-group flow diagram, which includes the stable and unstable fixed points corresponding to ${\cal M}_5$ and ${\cal M}_6$ in the minimal models of the conformal field theory. We perform numerical transfer-matrix calculations to determine a global phase diagram and also to proffer evidence to check our prediction.