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arXiv:cond-mat/9506050 · Physical Review Letters

Nonequilibrium Dynamics following a Quench to the Critical Point in a Semi-infinite System

Satya N. Majumdar, Anirvan M. Sengupta

Published Mar 25, 1996• 18 citations
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Abstract

We study the nonequilibrium dynamics (purely dissipative and relaxational) in a semi-infinite system following a quench from the high temperature disordered phase to its critical temperature. We show that the local autocorrelation near the surface of a semi-infinite system decays algebraically in time with a new exponent which is different from the bulk. We calculate this new nonequilibrium surface exponent in several cases, both analytically and numerically.

DOI
10.1103/physrevlett.76.2394

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We study the nonequilibrium dynamics (purely dissipative and relaxational) in a semi-infinite system following a quench from the high temperature disordered phase to its critical temperature. We show that the local autocorrelation near the surface of a semi-infinite system decays algebraically in time with a new exponent which is different from the bulk. We calculate this new nonequilibrium surface exponent in several cases, both analytically and numerically.
We study the time evolution of classical spin systems with purely relaxational dynamics, quenched from $T\ensuremath{\gg}{T}_{c}$ to the critical point, in the semi-infinite geometry. Shortly after the quench, as in the bulk, a nonequilibrium regime governed by universal power laws is also found near the surface. We show for "ordinary" and "special" transitions that the corresponding critical exponents differ from their bulk values, but can be expressed via scaling relations in terms of known bulk and surface exponents. To corroborate our scaling analysis, we present perturbative ($\ensuremath{\epsilon}$-expansion) and Monte Carlo results.
Nonequilibrium surface autocorrelation and autoresponse functions are studied numerically in semi-infinite critical systems in the dynamical scaling regime. Dynamical critical behavior is examined for a nonconserved order parameter in semi-infinite two- and three-dimensional Ising models as well as in the Hilhorst--van Leeuwen model. The latter model permits a systematic study of surface aging phenomena, as the surface critical exponents change continuously as function of a model parameter. The scaling behavior of surface two-time quantities is investigated and scaling functions are confronted with predictions coming from the theory of local scale invariance. Furthermore, surface fluctuation-dissipation ratios are computed and their asymptotic values are shown to depend on the values of surface critical exponents.
We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and quenched into the critical point. Using Monte Carlo simulations we measure single spin relaxation and autocorrelations, as well as manifold autocorrelations and persistence. We show that, depending on the decay of critical static correlations, the short time dynamics can be of two kinds. For slow decay of local correlations the usual domain growth process takes place with nonstationary and algebraic dynamical correlations. If, however, the local correlations decay sufficiently rapidly we have the so-called cluster dissolution scenario, in which case short time dynamical correlations are stationary and have a universal stretched exponential form. This latter phenomenon takes place in the surface of the three-dimensional Ising model and should be observable in real ferromagnets.
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We calculate the surface critical exponents of the ordinary transition occurring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation as well as in 4-epsilon dimensions. At d=4-epsilon we extend, up to the next-to-leading order, the previous first-order results of the square root of epsilon expansion by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. In both cases numerical estimates for surface exponents are computed using Padé approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.
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