Quasi-one-dimensional Ising models with defects of the "random local field" type: Imry-Ma phase in spaces with dimension higher than the lower critical one

TL;DR

This paper investigates the phase diagram of quasi-one-dimensional Ising models with random local field defects, demonstrating the potential for the Imry-Ma phase to occur in spaces with dimensions higher than the lower critical dimension, and analyzing the existence of long-range order.

Contribution

It shows that the Imry-Ma phase can appear in higher-dimensional spaces and explores the conditions for long-range order in Ising models with random fields at the critical dimension.

Findings

Imry-Ma phase can occur in spaces with dimension higher than the lower critical dimension.

Long-range order may exist in the Ising model with random fields at the critical dimension.

Phase diagram depends on temperature and defect concentration.

Abstract

The phase diagram in coordinates "temperature - concentration of defects" of quasi-one-dimensional Ising models with defects of the "random local field" type is investigated. The confrontation of the tendency to the emergence of the long-range order due to a weak interaction between one-dimensional spin chains and the tendency to the formation of the Imry-Ma phase in which the order parameter follows the fluctuations of the random field created by defects is studied. The possibility of the appearance of the Imry-Ma phase in a situation where the space dimension exceeds the lower critical dimension is shown. The question of the existence of the long-range order in the Ising model with random fields in space with the critical dimension dl = 2 is considered.