The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

Limit Theorems for Monomer–Dimer Mean-Field Models with Attractive Potential

“…In order to obtain an asymptotic expansion of (2.1), which allows us to obtain its scaling properties, we will use a connection between the monomer-dimer problem and Gaussian moments [2,14]. Following the same argument of [2] one finds Proposition 2.1.…”

A Mean-Field Monomer–Dimer Model with Randomness: Exact Solution and Rigorous Results

“…In this section we recall the definition of a monomer-dimer model with pure hard-core interaction and we show how to write its partition function as a Gaussian expectation. This representation, which will be extensively used in this work, was first proposed in [31] and is an immediate consequence of the Wick-Isserlis formula for Gaussian moments. As a first application we show in this section that the well-known Heilmann-Lieb recursion formula [16] for monomer-dimer models corresponds in fact to a Gaussian integration by parts.…”

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

“…where Z (0) N (b ′ ) denotes the partition function ZN (a = 0, b = b ′ ) of the model without attractive interaction. Now we use the Wick-Isserlis rule to decouple the hard-core interaction, as was shown in [5,28]. Choosing σ 2 = N −1 and A ⊆ VN in (18), the non-attractive partition function rewrites as…”