Hard Core entropy: lower bounds

TL;DR

This paper derives lower bounds for the entropy of the Hard Core Model on 2D lattices using an unbiased sequential fill-in method, providing insights into the measure of maximal entropy.

Contribution

It introduces a new unbiased sequential fill-in approach to estimate lower bounds for the Hard Core Model's entropy on 2D lattices.

Findings

Established lower bounds for the entropy of the Hard Core Model.

Provided detailed information on the support of the measure of maximal entropy.

Method allows arbitrarily good estimates for topological entropy.

Abstract

We establish lower bounds for the entropy of the Hard Core Model on a few 2d lattices $\scriptstyle {\rm {\bf L}}.$ In this model the allowed configurations inside $\scriptstyle \{0,1\}^{{\rm {\bf L}}}$ are the one's in which the nearest neighbor $\scriptstyle 1$'s are forbidden. Our method which is based on a sequential fill-in scheme is unbiassed and thereby yields in principle arbitrarily good estimates for the topological entropy. The procedure also gives some detailed information on the support of the measure of maximal entropy.