On Random Field Induced Ordering in the Classical XY Model

Abstract

Consider the classical XY model in a weak random external field pointing along the $Y$ axis with strength $\epsilon$. We study the behavior of this model as the range of the interaction is varied. We prove that in any dimension $d\ge 2$ and for all $\epsilon$ sufficiently small, there is a range $L=L(\epsilon )$ so that whenever the inverse temperature $\beta$ is larger than some $\beta (\epsilon )$, there is strong residual ordering along the $X$ direction.

30 pages

References in corpus (4)

• Order from Disorder in Graphene Quantum Hall Ferromagnet
• Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases
• Classical spin models with broken symmetry: Random Field Induced Order and Persistence of spontaneous magnetization in presence of a random field
• Loss and Recovery of Gibbsianness for XY models in external fields

Cited by in corpus (12)

• Breaking through the Mermin-Wagner limit in 2D van der Waals magnets
• Rigorous Results on the Bipartite Mean-Field Model
• Random Field Induced Order in Low Dimension
• Classical spin models with broken symmetry: Random Field Induced Order and Persistence of spontaneous magnetization in presence of a random field
• Discrete approximations to vector spin models
• Physical limitations of the Hohenberg-Mermin-Wagner theorem
• Spontaneous magnetization of quantum $XY$ spin model in joint presence of quenched and annealed disorder
• Order-from-disorder and critical scalings of spontaneous magnetization in random-field quantum spin systems
• Exactly Solvable Model of Randomly Coupled Twisted Superconducting Bilayers
• Decimations for Two-dimensional Ising and Rotator Models I
• Random-field-induced order in bosonic t-J model
• Uniqueness of gradient Gibbs measures with disorder