Frustrations on decorated planar lattices in Ising model

TL;DR

This paper investigates how magnetic frustrations arise in decorated planar lattices within the Ising model and explores their coexistence with long-range order using an exact analytical approach.

Contribution

It provides an exact analytical study of frustration phenomena in decorated lattices and reveals conditions for coexistence of frustration and magnetic order.

Findings

Magnetic frustrations exist in decorated lattices.

Frustrations influence thermodynamic functions.

Coexistence of frustrations and long-range order is possible.

Abstract

We study the frustration properties of the Ising model on several decorated lattices with arbitrary numbers of decorating spins on all bonds of the lattice within an exact analytical approach based on the Kramers--Wannier transfer-matrix technique. The existence of magnetic frustrations in such situations and their influence on the behavior of the thermodynamic functions of systems is shown. The most important result of our study is related to the description of the possible coexistence of frustrations and long-range magnetic order in partially ordered spin systems.