One dimensional spin glasses with potential decay \(1/r^{1+\epsilon}\). Absence of phase transitions and cluster properties
In this paper the one-dimensional Ising spin model with two-body random potential is considered decaying with the distance like \(1/r^{1+\epsilon}\). Assuming that the boundary conditions are independent of the random realisation of the interaction it is proved that with large probability the Gibbs expectation of an observable localized far away from the boundary of finite volume has a weak dependence on the boundary conditions. It is established also that the limiting Gibbs state exists which is a pure state and satisfies some mixing property. Moreover, with probability one, any two boundary conditions generate the same Gibbs state.
scientific article; zbMATH DE number 3996826
scientific article