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Generalized transformation for decorated spin models

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  • Rojas, Onofre
  • Valverde, J.S.
  • de Souza, S.M.

Abstract

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising model. We apply this transformation to a particular mixed spin-(1/2, 1) and (1/2, 2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin-S square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also includes combinations of three-body and four-body interactions; in particular we considered spin 1 and 2.

Suggested Citation

  • Rojas, Onofre & Valverde, J.S. & de Souza, S.M., 2009. "Generalized transformation for decorated spin models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1419-1430.
  • Handle: RePEc:eee:phsmap:v:388:y:2009:i:8:p:1419-1430
    DOI: 10.1016/j.physa.2008.12.063
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    Keywords

    Spin models; Decorated models;

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