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 $$\phi _\beta = \left\{ {_{\phi _\infty \circ v_\beta ,}^{\phi _0 \circ v_\beta ,} } \right. _{\beta > \beta _c .}^{0 \leqslant \beta< \beta _c } $$ .