Generalized Transformation for Decorated Spin Models

Abstract

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.

16 pages, 4 figures

References in corpus (6)

• Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains
• Thermodynamic properties of a tetramer ferro-ferro-antiferro-antiferromagnetic Ising-Heisenberg bond alternating chain as a model system for Cu(3-Clpy)${}_2$(N${}_3$)${}_2$
• Existence of the magnetization plateau in a class of exactly solvable Ising-Heisenberg chains
• Thermodynamic properties of the exactly solvable transverse Ising model on decorated planar lattices
• Exact solution of the mixed-spin Ising model on a decorated square lattice with two different kinds of decorating spins on horizontal and vertical bonds
• Spin Frustration in an Exactly Solvable Ising-Heisenberg Diamond Chain

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