Imry-Ma phase in O(n) models for space dimensions higher than the lower critical dimensionality

TL;DR

This paper demonstrates that the disordered Imry-Ma phase, characterized by the order parameter following random fields or anisotropies, can exist in higher-dimensional systems with continuous symmetry, under specific hyperplane conditions.

Contribution

It extends the understanding of the Imry-Ma phase to higher dimensions in O(n) models, identifying conditions involving hyperplanes and interaction strengths.

Findings

Imry-Ma phase exists in dimensions higher than 4.

Hyperplanes of dimension less than the lower critical dimension are crucial.

Interaction strength between hyperplanes determines phase stability.

Abstract

Systems with continuous symmetry of the vector order parameter containing defects of the "random local field" or "random local anisotropy" types are investigated. It is shown that the disordered Imry-Ma phase, in which the order parameter follows the spatial fluctuations of the random field or random anisotropy direction, can also occur in a coordinate space of dimension d higher than the lower critical dimension dl = 4. For this, the hyperplanes of dimension m < dl, must exist in the coordinate space in which there is a strong exchange interaction between spins, and the interaction between spins belonging to adjacent hyperplanes should not exceed a certain critical value.