Proof of entropic order in Generalized Ising Models

Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture. We further show that on arbitrary graphs, these models solve graph packing problems - crucially, the Maximum Independent Set optimisation problem. Due to the NP-hardness of this packing problem on generic graphs, some lattice systems will exhibit glassy phases. We call this phenomenon $entropic$ $glass$.