Rough Bounds for Emptiness Formation Probability in the 2d Dimer model using Reflection Positivity

TL;DR

This paper derives rough bounds for the emptiness formation probability in the 2D dimer model using reflection positivity, connecting classical and quantum spin systems.

Contribution

It applies reflection positivity techniques to establish bounds in the 2D dimer model, extending methods from 1D quantum models.

Findings

Established rough bounds for EFP in the 2D dimer model

Connected classical dimer model results to 1D quantum spin systems

Utilized reflection positivity as a key analytical tool

Abstract

We summarize how to obtain rough bounds for one version of the emptiness formation probability in the 2d dimer model. The methods we use are the same as have been developed to obtain EFP bounds in the 1d XXZ model in a paper with Crawford, Ng and one of the authors. A main tool is reflection positivity for the basic dimer model, as proved by Heilmann and Lieb. We also state the corollary for a 1d quantum spin system which Suzuki showed is related to the 2d Ising model.