Direct algebraic mapping transformation for decorated spin models

TL;DR

This paper introduces a direct algebraic transformation method for decorated spin models, simplifying calculations by mapping complex models onto effective spins without iterative procedures, applicable to various Ising and Ising-Heisenberg models.

Contribution

It presents a novel direct mapping transformation for decorated spin models, reducing computational complexity and enabling new analytical solutions for models with arbitrary coordination numbers.

Findings

Effective mapping for decorated Ising models

Extension to decorated Ising-Heisenberg models

New examples demonstrating the transformation

Abstract

In this article we propose a general transformation for decorated spin models. The advantage of this transformation is to perform a direct mapping of a decorated spin model onto another effective spin thus simplifying algebraic computations by avoiding the proliferation of unnecessary iterative transformations and parameters that might otherwise lead to transcendental equations. Direct mapping transformation is discussed in detail for decorated Ising spin models as well as for decorated Ising-Heisenberg spin models, with arbitrary coordination number and with some constrained Hamiltonian's parameter for systems with coordination number larger than 4 (3) with (without) spin inversion symmetry respectively. In order to illustrate this transformation we give several examples of this mapping transformation, where most of them were not explored yet.