A set of exactly solvable Ising models with half-odd-integer spin

Details A set of exactly solvable Ising models with half-odd-integer spin A set of exactly solvable Ising models with half-odd-integer spin

2008-05-05

arxiv.org/abs/0805.0572v3

Physics Letters A, Volume 373, Issue 15, 30 March 2009, Pages 1321-1324

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.physleta.2009.02.020

We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbour interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the {\it free fermion} condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S is given by $S+1/2$. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.

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