Absence of many states in realistic spin glasses

Abstract

Based on a simple scaling ansatz, the authors argue that no pure thermodynamic states other than the paramagnetic state and a pair of states in zero magnetic field which are related by a global spin flip can exist in short-range Ising spin glass models in any dimension. An analogous result should hold for XY and Heisenberg spin glasses, as well as for square-integrable long-range interactions.