The Breaking of Geometric Constraint of Classical Dimers on the Square Lattice

TL;DR

This paper investigates a classical dimer model on a square lattice, revealing a BKT transition under geometric constraints and a shift to a quasi first-order transition when constraints are removed, using novel algorithms.

Contribution

It introduces a new cluster updating algorithm and demonstrates the transition change when geometric constraints are broken in the dimer model.

Findings

Identified BKT transition in constrained dimer model.

Discovered transition shifts to quasi first-order when constraints are removed.

Developed an edged cluster algorithm for efficient topological sampling.

Abstract

We study a model of two-dimensional classical dimers on the square lattice with strong geometric constraints (there is exactly one bond with the nearest point for every point in the lattice). This model corresponds to the quantum dimer model suggested by D.S. Rokhsar and S.A. Kivelson (1988). We use the directed-loop algorithm to show the system undergoes a Berezinskii-Kostelitz Thousless transition (BKT transition) in finite temperatures. After that, if we destroy the geometric constraint of dimers, the topological transition will transfer to a quasi one-order transition. For the dimer updates, we also introduce a new cluster updating algorithm called the edged cluster algorithm. By this method, we succeed in rapidly traversing the winding (topological) sections uniformly and widening the effective matrical ensemble to include more topological sections.