Correlations and confinement in non-planar two-dimensional dimer models

TL;DR

This study investigates how extending the links in two-dimensional dimer models affects correlations and confinement, revealing persistent algebraic correlations with longer dimers and exponential decay with even small fractions of next-nearest neighbors.

Contribution

It demonstrates that longer bipartite dimers preserve algebraic correlations, while small fractions of next-nearest-neighbor dimers induce exponential decay and deconfinement.

Findings

Algebraic correlations persist with longer dimers.

Logarithmic peaks vanish in the structure factor.

Small fractions of next-nearest dimers cause exponential decay.

Abstract

We study classical hard-core dimer models on the square lattice with links extending beyond nearest-neighbors. Numerically, using a directed-loop Monte Carlo algorithm, we find that, in the presence of longer dimers preserving the bipartite graph structure, algebraic correlations persist. While the confinement exponent for monomers drifts, the leading decay of dimer correlations remains 1/r^2, although the logarithmic peaks present in the dimer structure factor of the nearest-neighbour model vanish. By contrast, an arbitrarily small fraction of next-nearest-neighbor dimers leads to the onset of exponential dimer correlations and deconfinement. We discuss these results in the framework of effective theories, and provide an approximate but accurate analytical expression for the dimer correlations.