Some Remarks on Almost Gibbs States

Abstract

We investigate possible ways to generalize the concept of Gibbs states. For classical lattice systems we do so by modifying the configuration space and considering the continuity of conditional probabilities thereupon. For quantum systems we are led by the structure that can be inferred from considering the correlation functions of the two-dimensional (ferromagnetic) Ising model as so-called ‘classical’ states on a quantum system. In the latter context our notion of an almost Gibbs state coincides with the notion of a state that does not satisfy the Kubo-Martin-Schwinger boundary condition but instead has only the structure that follows from Tomita’s theorem for so-called separating states on the observables.