Specific Heat of Ising Model with Holes: Mathematical Details Using Dimer Approaches

TL;DR

This paper employs dimer methods to analyze the specific heat of a modified Ising model with holes, revealing how connectivity and proximity influence thermodynamic properties.

Contribution

It introduces a dimer-based approach to compute free energy for an Ising model with complex connectivity, including horizontal strips and vertical strings.

Findings

Derived free energy as a single integral expression.

Obtained results for critical temperatures.

Analyzed effects of connectivity and proximity on specific heat.

Abstract

In this paper, we use the dimer method to obtain the free energy of Ising models consisting of repeated horizontal strips of width $m$ connected by sequences of vertical strings of length $n$ mutually separated by distance $N$, with $N$ arbitrary, to investigate the effects of connectivity and proximity on the specific heat. The decoration method is used to transform the strings of $n+1$ spins interacting with their nearest neighbors with coupling $J$ into a pair with coupling $\bar J$ between the two spins. The free energy per site is given as a single integral and some results for critical temperatures are derived.