Exact solution of the mixed-spin Ising model on a decorated square lattice with two different kinds of decorating spins on horizontal and vertical bonds

TL;DR

This paper provides an exact solution for a mixed-spin Ising model on a decorated square lattice, revealing unique critical behaviors influenced by single-ion anisotropy and the nature of decorating spins.

Contribution

It introduces an exact mapping method for solving the mixed-spin Ising model with different decorating spins on a decorated lattice, highlighting novel critical phenomena.

Findings

Revealed peculiar critical behavior due to single-ion anisotropy.

Discovered spontaneous ordering even with non-magnetic S=0 spins.

Described temperature dependence of magnetization in various ferrimagnetic states.

Abstract

The mixed spin-(1/2, S_B, S_C) Ising model on a decorated square lattice with two different kinds of decorating spins S_B and S_C placed on its horizontal and vertical bonds, respectively, is exactly solved by establishing a precise mapping relationship with the corresponding spin-1/2 Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy acting on both types of decorating spins S_B and S_C is examined in particular. If decorating spins S_B and S_C are integer and half-odd-integer, respectively, or if the reverse is the case, the model under investigation displays a very peculiar critical behavior beared on the spontaneously ordered 'quasi-1D' spin system, which appears as a result of the single-ion anisotropy strengthening. We have found convincing evidence that this remarkable spontaneous ordering virtually arises even though all integer-valued decorating spins tend towards their 'non-magnetic' spin state S=0 and the system becomes disordered only upon further increase of the single-ion anisotropy. The single-ion anisotropy parameter is also at an origin of various temperature dependences of the total magnetization when imposing the pure ferrimagnetic or the mixed ferro-ferrimagnetic character of the spin arrangement.