Statistical Mechanics of Interfering Links

Abstract

We consider the statistical mechanics of interfering transmissions in a wireless communications protocol. In this case, a connection between two nodes requires all other nodes within communication distance of the given two nodes to remain quiet on the given channel. This leads to an interesting problem of dimers on a lattice, with a restriction that no two dimers can overlap or be nearest neighbors. We consider both an equilibrium and a non-equilibrium, "greedy" dynamics for the links; the equilibrium properties of the model are found to exhibit an interesting spin glass transition at maximum density on certain lattices, while the greedy construction is related to the problem of random sequential adsorption.