The β-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. ► The β-expansion coefficients of the HFE of any one-dimensional (1D) effective (dressed) Hamiltonian. ► 1D models defined on the Hilbert spaces of super-sites. ► The β-expansion of the HFE of the 1D staggered longitudinal spin-S Ising model. ► Comparison of the thermodynamics of the standard spin-S Ising model and its staggered version.