Long-range order induced by random fields in two-dimensional O(n) models, and the Imry-Ma state

Abstract

The influence of defects of the "random local field" type with an anisotropic distribution of random fields on two-dimensional models with continuous symmetry of the vector order parameter is considered. In the case of weak anisotropy of random fields, with decreasing temperature there takes place a smooth transition from the paramagnetic phase with dynamic fluctuations of the order parameter to the Imry-Ma phase with static fluctuations caused by fluctuations of the random field of defects. In the case of strong anisotropy of random fields, defects lead to an effective decrease in the number of components of the order parameter and the appearance of a phase transition to an ordered state at finite temperature. It is shown that in the case of the defect-free two-dimensional X-Y model, the appearance of an arbitrarily weak anisotropy in the two-dimensional space of the order parameter completely eliminates the appearance of the Berezinsky-Kosterlitz-Thouless phase and gives rise to the phase with the long-range order.

arXiv comment16 pages, 3 figures

References in corpus (4)

• Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases
• A Mechanism of Long-Range Order Induced by Random Local Fields: Effective Anisotropy Created by Defects
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Cited by in corpus (2)

• 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
• Two-dimensional O(n) Models with Defects of "Random Local Anisotropy" Type