The anisotropic XY model on the 1D alternating superlattice

The anisotropic XY-model in a transverse field (s = 1/2) on the one-dimensi onal alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan-Wigner transform ation which maps the system onto a non-interacting fermion gas. The exact e xcitation spectrum is determined by reducing the problem to a diagonalizati on of a block matrix. and it is shown that it is numerically identical to t he one obtained by using the approximate transfer matrix method. The induce d magnetization and the susceptibility chi (approximate to approximate to) are determined as a function of the transverse field, and it is shown that, at T = 0. the susceptibility presents multiple singularities. It is also s hown, as expected, that this critical behaviour driven by transverse field belongs to the same universality class of the model on the alternating chai n. (C) 2001 Elsevier Science B.V. All rights reserved.