Exact results of the mixed-spin Ising model on a decorated square lattice with two different decorating spins of integer magnitudes

TL;DR

This paper provides exact analytical results for a mixed-spin Ising model on a decorated square lattice, revealing unique critical behavior and the impact of single-ion anisotropy on magnetic properties.

Contribution

It introduces an exact solution for a mixed-spin Ising model with two different decorating spins, highlighting novel spontaneous order phenomena.

Findings

Spontaneous order occurs when decorating spins approach non-magnetic states.

Disorder sets in with increasing single-ion anisotropy.

Temperature dependence of magnetization is significantly affected by anisotropy.

Abstract

The mixed-spin Ising model on a decorated square lattice with two different decorating spins of the integer magnitudes S_B = 1 and S_C = 2 placed on horizontal and vertical bonds of the lattice, respectively, is examined within an exact analytical approach based on the generalized decoration-iteration mapping transformation. Besides the ground-state analysis, finite-temperature properties of the system are also investigated in detail. The most interesting numerical result to emerge from our study relates to a striking critical behaviour of the spontaneously ordered 'quasi-1D' spin system. It was found that this quite remarkable spontaneous order arises when one sub-lattice of the decorating spins (either S_B or S_C) tends towards their 'non-magnetic' spin state S = 0 and the system becomes disordered only upon further single-ion anisotropy strengthening. The effect of single-ion anisotropy upon the temperature dependence of the total and sub-lattice magnetization is also particularly investigated.