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/0612147 · The European Physical Journal B

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

Published Mar 1, 2007• 14 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2007-00095-5

Related papers

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

Christopher Mudry, Xiao-Gang Wen

arXiv:cond-mat/9712146•Nuclear Physics B•Jun 1, 1999•24 citations

Quasi-long-range order in the 2D XY model with random phase shifts

Vincenzo Alba, Andrea Pelissetto, Ettore Vicari

We study the square-lattice XY model in the presence of random phase shifts. We consider two different disorder distributions with zero average shift and investigate the low-temperature quasi-long-range order phase which occurs for sufficiently low disorder. By means of Monte Carlo simulations we determine several universal quantities which are then compared with the analytic predictions of the random spin-wave theory. We observe a very good agreement which indicates that the universal long-distance behavior in the whole low-disorder low-temperature phase is fully described by the random spin-wave theory.

arXiv:0901.4682•Journal of Physics A Mathematical and Theoretical•Jul 6, 2009•6 citations

Phase Transition in the 2D XY Model with 3-Fold Nematic Interactions

Nguyễn Thị Minh Huyền, Lưu Bích Linh, Bui Thi Toan Thu +5 more

In this work the results of the study on a generalization of the XY model with an additional q-fold nematic-like term through Monte Carlo simulations in two dimensions (2D) have been presented. While the conventional 2D XY model has only integer vortexes, the generalized 2D XY model has both integer and non-integer 1/q vortexes, making the phase diagram of the generalized 2D XY model is much richer than that of the conventional 2D XY model. Here, we located the phase transition between the disordered phase (P), the quasi-long-range order phase (F), and the nematic phase (N) for the case of q = 3. We provided the numerical evidence to clarify the N−F phase transition of either the first-ordered or second-ordered phase transition. The results showed that the N−F phase transition is the second-ordered, not the first-order phase transition.

VNU Journal of Science Mathematics - Physics•Jun 24, 2022•0 citations

Numerical simulation of the XY-model on a two-dimensional random lattice

J.F. McCarthy

Nuclear Physics B•Nov 1, 1986•19 citations

Absence of Reentrance in the Two-Dimensional XY-Model with Positional Disorder

Mai Suan Li

We show, that the 2D XY-model with random phase shifts exhibits for low temperature and small disorder a phase with quasi-long-range order, and that the transition to the disordered phase is not reentrant. These results are obtained by heuristic arguments, an analytical renormalization group (RG) calculation, and a numerical Migdal-Kadanoff renormalization group treatment.

•Aug 20, 1995•0 citations

Ground-state long-range order in the two-dimensional XXZ model

秀稔 西森, Hidetoshi Nishimori, 之康 尾関 +1 more

•Mar 1, 1989•0 citations
We study the square-lattice XY model in the presence of random phase shifts. We consider two different disorder distributions with zero average shift and investigate the low-temperature quasi-long-range order phase which occurs for sufficiently low disorder. By means of Monte Carlo simulations we determine several universal quantities which are then compared with the analytic predictions of the random spin-wave theory. We observe a very good agreement which indicates that the universal long-distance behavior in the whole low-disorder low-temperature phase is fully described by the random spin-wave theory.
In this work the results of the study on a generalization of the XY model with an additional q-fold nematic-like term through Monte Carlo simulations in two dimensions (2D) have been presented. While the conventional 2D XY model has only integer vortexes, the generalized 2D XY model has both integer and non-integer 1/q vortexes, making the phase diagram of the generalized 2D XY model is much richer than that of the conventional 2D XY model. Here, we located the phase transition between the disordered phase (P), the quasi-long-range order phase (F), and the nematic phase (N) for the case of q = 3. We provided the numerical evidence to clarify the N−F phase transition of either the first-ordered or second-ordered phase transition. The results showed that the N−F phase transition is the second-ordered, not the first-order phase transition.