Direct algebraic mapping transformation for decorated spin models

In this paper, 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 before.