Frustration and ordering in Ising chain in an external magnetic field with third-neighbor interactions

TL;DR

This paper analyzes the frustration phenomena and magnetic properties of a one-dimensional Ising model with third-neighbor interactions under an external magnetic field, providing exact solutions and phase diagrams.

Contribution

It offers exact analytical expressions for thermodynamic functions and a detailed magnetic phase diagram considering third-neighbor interactions and frustration effects.

Findings

Identified conditions for magnetic frustration based on exchange interactions and magnetic field.

Derived exact thermodynamic functions using the transfer-matrix method.

Revealed various behaviors of entropy, magnetization, and susceptibility in different regimes.

Abstract

In this paper, the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice in an external magnetic field are investigated, taking into account the exchange interactions of atomic spins at the sites of the first, second, and third neighbors. Exact analytical expressions for the thermodynamic functions of the system are obtained by the Kramers--Wannier transfer-matrix method. A magnetic phase diagram of the ground state of such a spin system is constructed and studied thoroughly. The points and lines of frustrations of the system depending on the values and signs of exchange interactions and on an external magnetic field are found. The criteria for the occurrence of magnetic frustrations in the presence of competition between the energies of exchange interactions and an external magnetic field are formulated. The peculiar features are investigated and the values of entropy and magnetization of the ground state of this model are obtained in the frustration regime and beyond it. Various types of behavior of entropy, magnetization, and magnetic susceptibility depending on the model parameters are revealed.