Close-packed dimers on the kagome lattice: Finite lattices and the Grassmannian approach

TL;DR

This paper extends the exact enumeration of close-packed dimers on the kagome lattice to finite lattices with various boundary conditions and asymmetric weights, and introduces a Grassmannian approach for analysis.

Contribution

It provides detailed correlation function analysis, finite lattice results, and a Grassmannian functional integral formulation for kagome lattice dimers.

Findings

Finite lattice results are simple for symmetric weights.

Correlation functions are explicitly analyzed.

Grassmannian approach is formulated and applied.

Abstract

In a recent paper [ F. Wang and F. Y. Wu, Phys. Rev. E 75 (2007) 040105(R) ] we reported exact results on the enumeration of close-packed dimers on an infinite kagome lattice. We computed the per-dimer free energy using both the Pfaffian approach and a vertex-model formulation, and found the result given by a simple expression. We also reported results on dimer-dimer correlations without giving details. In this paper we present details of the correlation function analysis. In addition, we extend the exact enumeration to finite lattices under two different boundary conditions and with asymmetric dimer weights. For symmetric dimer weights the finite-lattice results are again simple, and we show that they can be understood using a spin variable mapping. We also describe the formulation of a Grassmannian functional integral approach and apply it to the kagome lattice.