Nonergodic dynamics of the two-dimensional random-phase sine-Gordon model: Applications to vortex-glass arrays and disordered-substrate surfaces

Journal Article · Wed Feb 01 00:00:00 EST 1995 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.51.3305· OSTI ID:6641926

Cule, D; Shapir, Y ^[1]

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1. Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States) Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (United States)

The dynamics of the random-phase sine-Gordon model, which describes two-dimensional vortex-glass arrays and crystalline surfaces on disordered substrates, is investigated using the self-consistent Hartree approximation. The fluctuation-dissipation theorem is violated below the critical temperature [ital T][sub [ital c]] for large time [ital t][gt][ital t][sup *] where [ital t][sup *] diverges in the thermodynamic limit. While above [ital T][sub [ital c]] the averaged autocorrelation function diverges as [ital T]ln([ital t]), for [ital T][lt][ital T][sub [ital c]] it approaches a finite value [ital q][sup *][similar to]1/([ital T][sub [ital c]][minus][ital T]) as [ital q]([ital t])=[ital q][sup *][minus][ital c]([ital t]/[ital t][sup *])[sup [minus][nu]] (for [ital t][r arrow][ital t][sup *]) where [nu] is a temperature-dependent exponent. On larger time scales [ital t][gt][ital t][sup *] the dynamics becomes nonergodic. The static correlations behave as [similar to][ital T]ln[vert bar][ital [rvec x]][vert bar] for [ital T][gt][ital T][sub [ital c]] and for [ital T][lt][ital T][sub [ital c]] when [ital x][lt][xi][sup *] with [xi][sup *][similar to]exp[l brace][ital A]/([ital T][sub [ital c]][minus][ital T])[r brace]. For scales [ital x][gt][xi][sup *], they behave as [similar to][ital m][sup [minus]1][ital T]ln[vert bar][ital [rvec x]][vert bar] where [ital m][approx][ital T]/[ital T][sub [ital c]] near [ital T][sub [ital c]], in general agreement with the variational replica-symmetry breaking approach and with recent simulations of the disordered-substrate surface. For strong coupling the transition becomes first order.

• OSTI ID: 6641926
• Journal Information: Physical Review, B: Condensed Matter; (United States), Vol. 51:5; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
SINE-GORDON EQUATION
SELF-CONSISTENT FIELD
ERGODIC HYPOTHESIS
MIXED STATE
SURFACES
SYMMETRY BREAKING
TEMPERATURE DEPENDENCE
TWO-DIMENSIONAL CALCULATIONS
TYPE-II SUPERCONDUCTORS
EQUATIONS
FIELD EQUATIONS
HYPOTHESIS
SUPERCONDUCTORS
665000* - Physics of Condensed Matter- (1992-)