undirected graph G=(V,E) monomer-dimer model:set of all matchings M(G) partition function Z(G)=∑XM M∈M(G) λXMI Gibbs distribution (M)= ZGZ￾(G) = X M2M(G) ￾|M| monomer-dimer model: M(G) undirected graph G = (V,E) set of all matchings partition function µ(M) = ￾|M| Z￾(G) Gibbs distribution