Deconfinement and criticality in extended two-dimensional dimer models

TL;DR

This study investigates how extending the range of dimers in a 2D square lattice affects confinement and criticality, revealing deconfinement with minimal next-nearest-neighbor dimers and persistent critical correlations.

Contribution

It demonstrates that even a small fraction of extended dimers induces deconfinement, and explores the non-universality of the confinement exponent in such models.

Findings

Small next-nearest-neighbor dimers cause deconfinement.

Critical dimer-dimer correlations decay as r^{-2}.

Confinement exponent is non-universal.

Abstract

A square-lattice hard-core dimer model with links extending beyond nearest-neighbors is studied using a directed-loop Monte Carlo method. An arbitrarily small fraction of next-nearest-neighbor dimers is found to cause deconfinement, whereas a critical state with $r^{-2}$ distance dependence of the dimer-dimer correlations persists in the presence of longer dimers preserving the bipartite graph structure. However, the critical confinement exponent governing the correlation of two test monomers is non-universal. Implications for resonating-valence-bond states are discussed.