Field-Theory Approaches to Nonequilibrium Dynamics

Täuber, Uwe C.

doi:10.1007/3-540-69684-9_7

Cited by 61 publications

(46 citation statements)

References 82 publications

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“…We will specifically construct a dynamic perturbation theory expansion and determine the universal scaling behavior along with the dynamic critical exponents for the relaxational models A and B with non-conserved and conserved order parameter, respectively; for more in-depth treatments, the reader is referred to Refs. [17]- [19] and [9, chaps. 4,5].…”

Section: Critical Dynamicsmentioning

confidence: 99%

Renormalization Group: Applications in Statistical Physics

Täuber

2012

Nuclear Physics B - Proceedings Supplements

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These notes aim to provide a concise pedagogical introduction to some important applications of the renormalization group in statistical physics. After briefly reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena near continuous phase transitions in thermal equilibrium, Wilson's momentum shell renormalization group method is presented, and the critical exponents for the scalar Φ 4 model are determined to first order in a dimensional expansion about the upper critical dimension d c = 4. Subsequently, the physically equivalent but technically more versatile field-theoretic formulation of the perturbational renormalization group for static critical phenomena is described. It is explained how the emergence of scale invariance connects ultraviolet divergences to infrared singularities, and the renormalization group equation is employed to compute the critical exponents for the O(n)-symmetric Landau-Ginzburg-Wilson theory to lowest non-trivial order in the expansion. The second part of this overview is devoted to field theory representations of non-linear stochastic dynamical systems, and the application of renormalization group tools to critical dynamics. Dynamic critical phenomena in systems near equilibrium are efficiently captured through Langevin stochastic equations of motion, and their mapping onto the Janssen-De Dominicis response functional, as exemplified by the field-theoretic treatment of purely relaxational models with non-conserved (model A) and conserved order parameter (model B). As examples for other universality classes, the Langevin description and scaling exponents for isotropic ferromagnets at the critical point (model J) and for driven diffusive non-equilibrium systems are discussed. Finally, an outlook is presented to scale-invariant phenomena and non-equilibrium phase transitions in interacting particle systems. It is shown how the stochastic master equation associated with chemical reactions or population dynamics models can be mapped onto imaginary-time, non-Hermitian "quantum" mechanics. In the continuum limit, this Doi-Peliti Hamiltonian is in turn represented through a coherent-state path integral action, which allows an efficient and powerful renormalization group analysis of, e.g., diffusion-limited annihilation processes, and of phase transitions from active to inactive, absorbing states.

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Section: Critical Dynamicsmentioning

confidence: 99%

Renormalization Group: Applications in Statistical Physics

Täuber

2012

Nuclear Physics B - Proceedings Supplements

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“…Readers unfamiliar with the tools of field theory are directed to one of the standard texts [22]. A review of field theory for non-equilibrium dynamics is [23].…”

Section: Introductionmentioning

confidence: 99%

Correlations, fluctuations, and stability of a finite-size network of coupled oscillators

Buice

Chow

2007

Phys. Rev. E

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The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N , where N is the number of oscillators. The N → ∞ limit of this theory is what is traditionally called mean field theory for the Kuramoto model.

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“…Detailed discussions of the technical aspect of field-theoretic DRG calculations are well documented in the literature; see, e.g., Refs. [10,20]. In order to set up the background let us examine the linearized version of the model equations (8) together with the noise correlations (5) at τ = 0 by dropping all the nonlinear terms (u = 0).…”

Section: Nonequilibrium Steady Statesmentioning

confidence: 99%

Continuous universality in nonequilibrium relaxational dynamics of O(2) symmetric systems

Sarkar

Basu

2012

Phys. Rev. E

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We elucidate a nonconserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a nonzero noise cross correlation of amplitude D(×) in a stochastic Langevin description of the system, while maintaining the O(2) symmetry of the order parameter space. By performing dynamic renormalization group calculations in a field-theoretic set up, we analyze the ensuing nonequilibrium steady states and evaluate the scaling exponents near the critical point, which now depend explicitly on D(×). Since the latter remains unrenormalized, we obtain universality classes varying continuously with D(×). More interestingly, by changing D(×) continuously from zero, we can make our system move away from its equilibrium behavior (i.e., when D(×)=0) continuously and incrementally.

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Field-Theory Approaches to Nonequilibrium Dynamics

Cited by 61 publications

References 82 publications

Renormalization Group: Applications in Statistical Physics

Renormalization Group: Applications in Statistical Physics

Correlations, fluctuations, and stability of a finite-size network of coupled oscillators

Continuous universality in nonequilibrium relaxational dynamics of O(2) symmetric systems

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