Ground states for nonuniform periodic Ising chains

TL;DR

This paper generalizes the understanding of ground states in periodic Ising chains with nonuniform spins and long-range interactions, highlighting the effects of translational invariance and parity on ground state structures.

Contribution

It extends Morita's work to chains with varying spins and distant interactions, providing a comprehensive analysis of ground states and their degeneracies under these conditions.

Findings

Ground states depend on chain periodicity and spin variation.

Degeneracies and nonregular states can occur under certain conditions.

Ground state diagrams are constructed for various cases.

Abstract

We give a generalization of Morita's works on ground states of Ising chains, for chains with a periodic structure with different spins, and distant neighbor interactions. The main assumption is translational invariance. The length of the irreducible blocks is a multiple of the period of the chain. In the case of parity invariance, it restricts the length in general only in the diatomic case. There are degenerated states and under certain circumstances there could be nonregular ground states. We illustrate the results and give the ground state diagrams in several cases.