On aC*-algebra approach to phase transition in the two-dimensional Ising model. II

We investigate the statesφ _β on theC*-algebra of Pauli spins on a one-dimensional lattice (infinitely extended in both directions) which give rise to the thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model (with nearest neighbour interaction) at inverse temperature β. We show that if β _c is the known inverse critical temperature, then there exists a family {v _β :β≠β _c } of automorphisms of the Pauli algebra such that $$phi _beta = left{ {_{phi _infty circ v_beta ,}^{phi _0 circ v_beta ,} } right. _{beta > beta _c .}^{0 leqslant beta< beta _c } $$ .