Roughening and super-roughening in the ordered and random two-dimensional sine-Gordon models

Journal Article · Fri Sep 01 04:00:00 EDT 2000 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.62.3219· OSTI ID:20217617

Sanchez, Angel ^[1]; Bishop, A R ^[2]; Moro, Esteban ^[3]

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1. Grupo Interdisciplinar de Sistemas Complicados (GISC), Departamento de Matematicas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganes, Madrid, (Spain)
2. Theoretical Division and Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
3. Theoretical Physics Department, University of Oxford, 1 Keble Road, Oxford OX1 3NP, (United Kingdom)

We present a comparative numerical study of the ordered and the random two-dimensional sine-Gordon models on a lattice. We analytically compute the main features of the expected high-temperature phase of both models, described by the Edwards-Wilkinson equation. We then use those results to locate the transition temperatures of both models in our Langevin dynamics simulations. We show that our results reconcile previous contradictory numerical works concerning the super-roughening transition in the random sine-Gordon model. We also find evidence supporting the existence of two different low-temperature phases for the disordered model. We discuss our results in view of the different analytical predictions available and comment on the nature of these two putative phases. (c) 2000 The American Physical Society.

• OSTI ID: 20217617
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 3 Vol. 62; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
LANGEVIN EQUATION
ORDER-DISORDER TRANSFORMATIONS
SINE-GORDON EQUATION
THEORETICAL DATA
TRANSITION TEMPERATURE