Classical spin models with broken symmetry: Random Field Induced Order and Persistence of spontaneous magnetization in presence of a random field

Abstract

We consider classical spin models of two- and three-dimensional spins with continuous symmetry and investigate the effect of a symmetry-breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean-field regime. We show, by perturbative calculations and numerical simulations, that although the continuous symmetry of the magnetization is lost due to disorder, the system still magnetizes in specific directions, albeit with a lower value as compared to the case without disorder. The critical temperature, at which the system starts magnetizing, as well as the magnetization at low and high temperature limits, in presence of disorder, are estimated. Moreover, we treat the SO(n) n-component spin model to obtain the generalized expressions for the near-critical scalings, which suggest that the effect of disorder in magnetization increases with increasing dimension. We also study the behavior of magnetization of the classical XY spin model in the presence of a constant magnetic field, in addition to the quenched disorder. We find that in presence of the uniform magnetic field, disorder may enhance the component of magnetization in the direction that is transverse to the disorder field.

arXiv comment18 pages, 12 figures, REVTeX4-1; significantly extends and improves upon the results in arXiv:0712.0829

References in corpus (24)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Disordered quantum gases under control
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Anderson localization in Bose-Einstein condensates
• Cold atoms in the presence of disorder
• On Larkin-Imry-Ma State of 3He-A in Aerogel
• Order from Disorder in Graphene Quantum Hall Ferromagnet
• Disorder-induced trapping versus Anderson localization in Bose-Einstein condensates expanding in disordered potentials
• Disordered ultracold atomic gases in optical lattices: A case study of Fermi-Bose mixtures
• Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases
• Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder
• Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder
• Disorder-Induced Order in Two-Component Bose-Einstein Condensates
• Transport regimes of cold gases in a two-dimensional anisotropic disorder
• Disorder-Induced Order in Quantum XY Chains
• Proof of Rounding by Quenched Disorder of First Order Transitions in Low-Dimensional Quantum Systems
• Disorder-Induced Phase Control in Superfluid Fermi-Bose Mixtures
• Two-component Bose gases with one-body and two-body couplings
• Random Field Induced Order in Low Dimension
• On Random Field Induced Ordering in the Classical XY Model
• The ground state of binary systems with a periodic modulation of the linear coupling
• Loss and Recovery of Gibbsianness for XY models in external fields
• Superfluid phases of 3He in aerogel
• Random-field-induced order in bosonic t-J model

Cited by in corpus (11)

• Inhomogeneous time-reversal symmetry breaking in ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$
• On Random Field Induced Ordering in the Classical XY Model
• Random Field Induced Order in Low Dimension
• Spontaneous magnetization of quantum $XY$ spin model in joint presence of quenched and annealed disorder
• Stark localization near Aubry-André criticality
• Order-from-disorder and critical scalings of spontaneous magnetization in random-field quantum spin systems
• Response of entanglement to annealed vis-à-vis quenched disorder in quantum spin models
• Trends of information backflow in disordered spin chains
• Bose-Einstein condensates in disordered potentials
• Localization with non-Hermitian off-diagonal disorder
• Imperfect Entangling Power of Quantum Gates