Finite-size corrections for the attractive mean-field monomer-dimer model

TL;DR

This paper derives explicit finite-size corrections for key thermodynamic quantities in an attractive mean-field monomer-dimer model, enhancing understanding of finite-volume effects in such systems.

Contribution

It introduces a two-dimensional integral representation for the partition function, allowing explicit calculation of finite-size corrections and their signs.

Findings

Explicit formulas for finite-size corrections to pressure, monomer density, and susceptibility.

Determination of the signs of corrections indicating monotonic convergence.

Next-to-leading order terms explicitly derived for each quantity.

Abstract

The finite volume correction for a mean-field monomer-dimer system with an attractive interaction are computed for the pressure density, the monomer density and the susceptibility. The results are obtained by introducing a two-dimensional integral representation for the partition function decoupling both the hard-core interaction and the attractive one. The next-to-leading terms for each of the mentioned quantities is explicitly derived as well as the value of their sign that is related to their monotonic convergence in the thermodynamic limit.