Non-Local Finite-Size Effects in the Dimer Model

TL;DR

This paper investigates how finite-size effects in the dimer model on an infinite strip depend on the parity of the width, revealing non-local features that relate boundary conditions to conformal field theory.

Contribution

It demonstrates that the parity of the lattice width influences boundary conditions and finite-size corrections, explained through the $c=-2$ logarithmic conformal field theory.

Findings

Finite-size corrections depend on the parity of N.

Changing N's parity alters boundary conditions.

Finite-size behaviors are explained by logarithmic conformal field theory.

Abstract

We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of $N$, and show that, because of certain non-local features present in the model, a change of parity of $N$ induces a change of boundary condition. Taking a careful account of this, these unusual finite-size behaviours can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.