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  • 1
    Digitale Medien
    Digitale Medien
    Biased Diffusion with Correlated Noise (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 569-586 
    Details
    ISSN: 1572-9613
    Schlagwort(e): nonequilibrium steady states ; driven diffusive systems ; correlated noise
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension d LR, the long-ranged noise is always relevant. In contrast, for d〈d LR, we find a “weak noise” regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004562408226
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  • 2
    Digitale Medien
    Digitale Medien
    Field Theory of Critical Behavior in Driven Diffusive Systems with Quenched Disorder (1999)
    Springer
    Journal of statistical physics 96 (1999), S. 817-859 
    Details
    ISSN: 1572-9613
    Schlagwort(e): driven diffusive systems ; nonequilibrium steady states ; lattice gas ; phase transitions ; field-theoretic renormalization group ; quenched disorder
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We present a field-theoretic renormalization-group study for the critical behavior of a uniformly driven diffusive system with quenched disorder, which is modeled by different kinds of potential barriers between sites. Due to their symmetry properties, these different realizations of the random potential barriers lead to three different models for the phase transition to transverse order and to one model for the phase transition to longitudinal order all belonging to distinct universality classes. In these four models, which have different upper critical dimensions d c, we find the critical scaling behavior of the vertex functions in spatial dimensions d〈d c. The deviation from purely diffusive behavior is characterized by the anomaly exponent η, which we calculate at first and second order, respectively, in ε=d c−d. In each model η turns out to be positive, which means superdiffusive spread of density fluctuations in the driving force direction.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004610726108
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  • 3
    Digitale Medien
    Digitale Medien
    Stochastisches Reaktionsmodell für einen Nichtgleichgewichts-Phasenübergang Stochastic Reaction Model for a Non-Equilibrium Phase Transition (1975)
    Springer
    The European physical journal 20 (1975), S. 338-338 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01352594
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  • 4
    Digitale Medien
    Digitale Medien
    Renormalized field theory of critical dynamics (1976)
    Springer
    The European physical journal 24 (1976), S. 113-127 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We formulate a Gell'Mann-Low-type renormalization group approach to the critical dynamics of stochastic models described by Langevin or Fokker-Planck equations including mode-coupling terms. Dynamical correlation and response functions are expressed in terms of path integrals, which are investigated by well-known methods of renormalized perturbation theory. Dynamical scaling laws and relations between static and dynamic critical exponents are derived. The leading temperature-dependence of correlation and response functions is obtained from the Kadanoff-Wilson short-distance expansion. We also consider corrections to dynamic scaling which are due to a finite lattice constant.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01312880
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  • 5
    Digitale Medien
    Digitale Medien
    Equation of motion and nonlinear response near the critical point (1976)
    Springer
    The European physical journal 25 (1976), S. 275-278 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract For a one-component (Ising-like) Ginzburg-Landau field we have derived an equation of motion which governs the behaviour of the order parameter nearT c . We present this equation in a general scaling form dictated by the renormalization group, and calculate the form explicitly to first order inε=4−d. There is a memory term in the result which in orderε contains the full nonlinear response of the order parameter. As a special case we obtain the linear response function for a nonvanishing external field.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01420890
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  • 6
    Digitale Medien
    Digitale Medien
    New universal short-time scaling behaviour of critical relaxation processes (1989)
    Springer
    The European physical journal 73 (1989), S. 539-549 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We study the critical relaxation properties of Model A (purely dissipative relaxation) starting from a macroscopically prepared initial state characterised by non-equilibrium values for order parameter and correlations. Using a renormalisation group approach we observe that even (macroscopically)early stages of the relaxation process display universal behaviour governed by a new, independent “initial slip” exponent. For large times, the system crosses over to the well-known long-time relaxation behaviour. The new exponent is calculated toO(ε2) in ε=4−d, whered is the spatial dimension of the system. The initial slip scaling form of general correlation and response functions as well as the order parameter is derived, exploiting a short-time operator expansion. The leading scaling behaviour is determined by initial states with sharp values of the order parameter. Non-vanishing correlations generate corrections to scaling.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01319383
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  • 7
    Digitale Medien
    Digitale Medien
    On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state (1981)
    Springer
    The European physical journal 42 (1981), S. 151-154 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g. Schlögl's first reaction) exhibit nevertheless a second order phase transition in non-zero dimensional macroscopic systems. The relation to Reggeon field theory is given more directly than by Grassberger et al. using the functional integral formalism of statistical dynamics. As a new result the correlation length exponent ν and the order parameter exponent β are found toO(ε2) in an ɛ-expansion around the upper critical dimensiond c=4.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01319549
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  • 8
    Digitale Medien
    Digitale Medien
    Field theory of critical behaviour in driven diffusive systems (1986)
    Springer
    The European physical journal 64 (1986), S. 503-514 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We present a field theoretic renormalisation group study for the critical behaviour of a diffusive system with a single conserved density subjected to an external driving force. The anisotropies induced by the external field require the introduction of two critical parameters associated with transverse and longitudinal order. The transition to transverse order is governed by a fixed point which is infrared stable below five dimensions. With the help of Ward-Takahashi identities based on Galilei invariance, we derive scaling forms for density correlation functions, critical exponents to all orders in ε=5−d, and the equation of state, taking care of a dangerous irrelevant composite operator. The transition is continuous and of mean-field type, with anomalous long-wavelength and long-time correlations in the longitudinal direction only. For the transition to longitudinal order, no infrared stable fixed point is found. An analysis of the mean-field equations indicates that the transition is discontinuous.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01312845
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  • 9
    Digitale Medien
    Digitale Medien
    Finite size scaling for directed percolation and related stochastic evolution processes (1988)
    Springer
    The European physical journal 71 (1988), S. 377-385 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Finite size scaling effects are investigated for certain evolution processes modelled by a one-component reaction-diffusion system with an absorbing state. The model possesses a non-equilibrium critical point, and the associated universality class includes directed bond percolation, cellular automata, Reggeon field theory and a stochastic version of Schlögl's first autocatalytic reaction scheme. Using renormalisation group techniques, we calculate the linear relaxation time in a cubic geometry of finite sizeL, with periodic boundary conditions imposed. The corresponding scaling behaviour toO(ɛ) (ɛ=4−d,d being the spatial dimension) is presented in universal form.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01312497
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  • 10
    Digitale Medien
    Digitale Medien
    Stability of transport (1972)
    Springer
    The European physical journal 253 (1972), S. 176-182 
    Details
    ISSN: 1434-601X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract It is shown that the stability criterion derived by Schlögl from statistical theory leads in the case of hydrodynamical transport states to a global stability criterion for a steady nonequilibrium state which leads under assumption of locality and for infinitesimal deviations from the steady state to the stability criterion of Glansdorff and Prigogine.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01379771
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