The β-expansion of periodic dressed chain models

We revisit the method of calculating the beta-expansion of the Helmholtz free energy of any one-dimensional (1D) Hamiltonian with invariance under space translations, presented in [O. Rojas, S.M. de Souza, M.T. Thomaz, J. Math. Phys. 43 (2002) 1390], extending this method to 1-D Hamiltonians that are invariant under translations along super-sites (sequences of I sites). The method is applicable, for instance, to spin models and bosonic/fermionic versions of Hubbard models, either quantum or classical. As an example, we focus on the staggered spin-S Ising model in the presence of a longitudinal magnetic field, comparing some of its thermodynamic functions to those of the standard Ising model. We show that for arbitrary values of spin (S is an element of (1, 3/2, 2, ...)) but distinct values of the coupling constant and the magnetic field, the specific heat and the z-component of the staggered and usual magnetizations can be well approximated by their respective thermodynamic function of the spin-1/2 models in a suitable interval of temperature. These approximations are valid for the standard Ising model as well as for the staggered model, the thermodynamics of which are known exactly. (C) 2011 Elsevier B.V. All rights reserved.