An operator theoretic approach to the brickwork Ising model with second-neighbor interactions

Using results on block Toeplitz matrices, in particular the Szegő–Widom limit theorem and Gohberg and Feldman’s convergence theorem for the finite section method, we compute the spontaneous magnetization of an Ising model. In this way, the transition from the ferromagnetic phase to the paramagnetic phase may be understood as the transition from invertibility to non-invertibility of a certain block Toeplitz operator associated with the model.