Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9712146 · Nuclear Physics B

Does quasi-long-range order in the two-dimensional XY model really survive weak random phase fluctuations?

Christopher Mudry, Xiao-Gang Wen

Published Jun 1, 1999• 24 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(99)00159-5

Related papers

The 2D XY model on a finite lattice with structural disorder: quasi-long-range ordering under realistic conditions

O. Kapikranian, Bertrand Berche, Yurij V. Holovatch

arXiv:cond-mat/0612147•The European Physical Journal B•Mar 1, 2007•14 citations

Nonequilibrium quasi-long-range order of a driven random-field O(N) model

Taiki Haga

We investigate three-dimensional O(N) spin models driven with a uniform velocity over a random field. Within a spin-wave approximation, it is shown that in the strong driving regime the model with N=2 exhibits a quasi-long-range order in which the spatial correlation function decays in a power-law form. Furthermore, for the cases that N=2 and 3, we numerically demonstrate a nonequilibrium phase transition between the quasi-long-range order phase and the disordered phase, which turns out to resemble the Kosterlitz-Thouless transition in the two-dimensional pure XY model in equilibrium.

arXiv:1504.06411•Physical Review E•Dec 7, 2015•7 citations

Phase Transitions in the Two-Dimensional Random Gauge XY Model

Petter Minnhagen, Beom Jun Kim, Petter Holme

APS•Mar 1, 2002•0 citations

Destruction of Bulk Ordering by Surface Randomness

D. E. Feldman, V. M. Vinokur

We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroys long-range order in the bulk, and, instead, quasi-long-range order emerges. Correlation functions are calculated exactly for the two- and three-dimensional XY models with surface randomness via the functional renormalization group. Even at strong quenched disorder the three-dimensional XY model possesses topological order. We also determine roughness of a domain wall in the presence of surface disorder.

arXiv:cond-mat/0205656•Physical Review Letters•Nov 12, 2002•17 citations

Unified Picture of Ferromagnetism, Quasi-Long-Range Order, and Criticality in Random-Field Models

Matthieu Tissier, Gilles Tarjus

By applying the recently developed nonperturbative functional renormalization group (FRG) approach, we study the interplay between ferromagnetism, quasi-long-range order (QLRO), and criticality in the d-dimensional random-field O(N) model in the whole (N, d) diagram. Even though the "dimensional reduction" property breaks down below some critical line, the topology of the phase diagram is found similar to that of the pure O(N) model, with, however, no equivalent of the Kosterlitz-Thouless transition. In addition, we obtain that QLRO, namely, a topologically ordered "Bragg glass" phase, is absent in the 3-dimensional random-field XY model. The nonperturbative results are supplemented by a perturbative FRG analysis to two loops around d = 4.

arXiv:cond-mat/0511096•Physical Review Letters•Mar 1, 2006•81 citations

First order transition in the random two-dimensional XY model

Mai Suan Li, Marek Cieplak

Physics Letters A•Jan 1, 1994•4 citations
We investigate three-dimensional O(N) spin models driven with a uniform velocity over a random field. Within a spin-wave approximation, it is shown that in the strong driving regime the model with N=2 exhibits a quasi-long-range order in which the spatial correlation function decays in a power-law form. Furthermore, for the cases that N=2 and 3, we numerically demonstrate a nonequilibrium phase transition between the quasi-long-range order phase and the disordered phase, which turns out to resemble the Kosterlitz-Thouless transition in the two-dimensional pure XY model in equilibrium.
We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroys long-range order in the bulk, and, instead, quasi-long-range order emerges. Correlation functions are calculated exactly for the two- and three-dimensional XY models with surface randomness via the functional renormalization group. Even at strong quenched disorder the three-dimensional XY model possesses topological order. We also determine roughness of a domain wall in the presence of surface disorder.
By applying the recently developed nonperturbative functional renormalization group (FRG) approach, we study the interplay between ferromagnetism, quasi-long-range order (QLRO), and criticality in the d-dimensional random-field O(N) model in the whole (N, d) diagram. Even though the "dimensional reduction" property breaks down below some critical line, the topology of the phase diagram is found similar to that of the pure O(N) model, with, however, no equivalent of the Kosterlitz-Thouless transition. In addition, we obtain that QLRO, namely, a topologically ordered "Bragg glass" phase, is absent in the 3-dimensional random-field XY model. The nonperturbative results are supplemented by a perturbative FRG analysis to two loops around d = 4.