Ising systems with random bonds

Dominicis, C. De; Stephen, Michael J.

doi:10.1088/0022-3719/11/24/008

Cited by 84 publications

(217 citation statements)

References 6 publications

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“…An alternative way to derive the results of this appendix is based on the Janssen-De Dominicis [53,54] path integral representation of (21). We refer to Ref.…”

Section: Ward Identitymentioning

confidence: 99%

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Mejía‐Monasterio

Muratore-Ginanneschi

2012

Phys. Rev. E

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We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4 − 2 ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's −5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the −5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

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“…An alternative way to derive the results of this appendix is based on the Janssen-De Dominicis [53,54] path integral representation of (21). We refer to Ref.…”

Section: Ward Identitymentioning

confidence: 99%

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Mejía‐Monasterio

Muratore-Ginanneschi

2012

Phys. Rev. E

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“…In this letter, we shall explore two generic types of detailed-balance violations, namely (a) coupling the order parameter and additional conserved quantities to heat baths with different temperatures, and (b) allowing for spatially anisotropic noise correlations for conserved variables. To determine their universal features, we map the Langevin dynamics for most of the models listed in Ref.[5] to a dynamic field theory [8], and employ standard renormalization group (RG) methods [6].In the theory of static critical phenomena, an analogous issue concerns the effect of terms that break the original order parameter symmetry, e.g., the influence of cubic anisotropies on the isotropic n-component Heisenberg model. There, the rotational symmetry is restored at criticality, provided n < n c ≈ 4 [9].…”

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confidence: 99%

Effects of Violating Detailed Balance on Critical Dynamics

2002

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We present an overview of the effects of detailed-balance violating perturbations on the universal static and dynamic scaling behavior near a critical point. It is demonstrated that the standard critical dynamics universality classes are generally quite robust: In systems with non-conserved order parameter, detailed balance is effectively restored at criticality. This also holds for models with conserved order parameter, and isotropic non-equilibrium perturbations. Genuinely novel features are found only for models with conserved order parameter and spatially anisotropic noise correlations.PACS numbers: 05.40.+j, 64.60.Ak, 64.60.Ht.One of the major goals in theoretical non-equilibrium physics has been the identification and classification of universality classes for the long-wavelength, long-time scaling behavior both near continuous dynamical phase transitions, and for systems displaying generic scale invariance. Indeed, through investigations of certain specific models, a number of prototypical non-equilibrium universality classes have been identified. A complementary approach is to study the influence of non-equilibrium perturbations on the known universality classes for equilibrium dynamical critical phenomena [5]. Equilibrium critical dynamics is concerned with the relaxational and reversible kinetics near a thermodynamic critical point at temperature T c , as generically described by the Landau-Ginzburg-Wilson (LGW) model for an n-component order parameter vector field S in d space dimensions [6]. In addition to the two independent static critical exponents, e.g. the correlation length exponent ν defined via ξ ∝ |τ | −ν (τ = T − T c ) and Fisher's exponent η for the algebraic decay of the two-point correlation function at criticality (T = T c ),, the order parameter relaxation is governed by a dynamic exponent z that describes critical slowing down: The characteristic time scale diverges as t ch ∝ |τ | −zν upon approaching the transition. This allows for time scale separation and thus a formulation of critical dynamics in terms of non-linear Langevin equations: The relevant 'slow' modes consist of the order parameter and all conserved quantities to which it is statically or dynamically coupled. All remaining 'fast' degrees of freedom are captured through an effective Gaussian white noise. Different values for z ensue depending on whether the order parameter is a conserved quantity or not, and on the additional conserved quantities present. The diffusive relaxation of the latter near criticality can either be characterized by the same exponent z as for the order parameter ('strong' dynamic scaling), or be given by different power laws ('weak' scaling) [5].In order to ensure relaxation towards thermal equilibrium at long times, as given by a Gibbs distribution, one has to carefully implement detailed-balance conditions. In the language of non-linear Langevin equations, these are (i) the Einstein relation between the relaxation constants and the noise strengths, and (ii) the condition that the probability cur...

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“…Instead of working with H directly, we recast H into the form of a dynamic functional [30,31,32]. This strategy is convenient because it simplifies the following calculations from the onset.…”

Section: A Diagrammatic Elementsmentioning

confidence: 99%

Untitled

Stenull

Janssen

2001

Journal of Statistical Physics

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We study resistor diode percolation at the transition from the non-percolating to the directed percolating phase. We derive a field theoretic Hamiltonian which describes not only geometric aspects of directed percolation clusters but also their electric transport properties. By employing renormalization group methods we determine the average two-port resistance of critical clusters, which is governed by a resistance exponent φ. We calculate φ to two-loop order.

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Ising systems with random bonds

Cited by 84 publications

References 6 publications

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Effects of Violating Detailed Balance on Critical Dynamics

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