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The β-expansion of periodic dressed chain models

Author

Listed:
  • Corrêa Silva, E.V.
  • de Souza, S.M.
  • Thomaz, M.T.

Abstract

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.

Suggested Citation

  • Corrêa Silva, E.V. & de Souza, S.M. & Thomaz, M.T., 2011. "The β-expansion of periodic dressed chain models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3108-3119.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:18:p:3108-3119
    DOI: 10.1016/j.physa.2011.04.018
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