Physics – Mathematical Physics
Scientific paper
2008-09-26
Physica A388:1419-1430,2009; Erratum-ibid.388:3282,2009
Physics
Mathematical Physics
16 pages, 4 figures
Scientific paper
10.1016/j.physa.2008.12.063 10.1
The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, 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 models. 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 include combinations of three-body and four-body interactions, particularly we considered spin 1 and 2.
de Souza Sergio Martins
Rojas Onofre
Valverde J. S.
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