Frustrations and orderings in Ising chain with multiple interactions

TL;DR

This paper investigates the frustration phenomena and magnetic orderings in a one-dimensional Ising model with multiple exchange interactions, providing exact solutions, phase diagrams, and criteria for frustration.

Contribution

It presents an exact solution for the Ising chain with multiple interactions and characterizes the conditions for magnetic frustration and ordering.

Findings

Exact solution of the model using transfer matrix method

Identification of ground state magnetic orderings

Criteria for the occurrence of magnetic frustration

Abstract

The frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice are investigated taking into account the exchange interactions of atomic spins at the sites of the first (nearest), second (next-nearest) and third neighbors. The exact solution of the model was obtained using the Kramers--Wannier transfer matrix method. The types of magnetic ordering of the ground state of the model are determined, and a magnetic phase diagram is constructed. Criteria are formulated for the occurrence of magnetic frustrations in the presence of competition between the energies of exchange interactions. Non-zero entropy values in the ground state of the frustrated system were found.