Bijection between spin $S=\frac{p^M-1}{2}$ and a cluster of $M$ spins $\sigma =\frac{p-1}{2}$

Abstract

We propose a general method by which a spin-$S$ is decomposed into spins less than $S$. We have obtain the exact mapping between spin $S=\frac{p^M-1}{2}$ and a cluster of $M$ spins $\sigma =\frac{p-1}{2}$. We have discuss the possible applications of such transformations. In particular we have show how a general $d+1$ dimensional spin-$\frac{p-1}{2}$ model with general interactions can be reduced to $d$-dimensional spin-$S$ model with $S=\frac{p^M-1}{2}$.

17 pages

References in corpus (3)

• A Spin - 3/2 Ising Model on a Square Lattice
• A set of exactly solvable Ising models with half-odd-integer spin
• Exact solution of a Z(4) gauge Potts model on planar lattices

Cited by in corpus (1)

• Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter-leg couplings