On a \(C^ *\)-algebra approach to phase transition in the two-dimensional Ising model. II
We investigate the states \(\phi_{\beta}\) on the \(C^*\)-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 \(\beta\). We show that if \(\beta_ c\) is the known inverse critical temperature, then there exists a family \(\{\nu_{\beta}:\beta \neq \beta_ c\}\) of automorhisms of the Pauli algebra such that \[ \phi_{\beta}=\phi_ 0\circ \nu_{\beta}\;if\;0\leq \beta <\beta_ c\quad and\quad =\phi_{\infty}\circ \nu_{\beta}\;if\;\beta >\beta_ c. \] [For part I see \textit{H. Araki} and the first named author, ibid. 91, 489-503 (1983; Zbl 0535.46046).]
C\({}^ *\)-algebra of Pauli spins on a one-dimensional lattice
thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model
scientific article; zbMATH DE number 3983888