The -expansion of periodic dressed chain models

We revisit the method of calculating the β -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 l 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 ∈ { 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.