States associated with the two-dimensional Ising model

A study is made of states on the algebra of 0uasilocal observables generated by the transfer matrix of the two-dimensional Ising model and its highest eigenvecto r in the infinite-volume limit. Both states are quasifree and the latter (“ground state”) is pure. The limit transfer matrix $P_{\infty}$ is also calculated in the space of the representation associated with the ground state. All the calculations are made by the Onsager–Kaufman method.