Critical dynamics: a field-theoretical approach

Folk, R.; Moser, G.

doi:10.1088/0305-4470/39/24/r01

Cited by 144 publications

(254 citation statements)

References 289 publications

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“…In such a coarse-grained picture, one writes down coupled stochastic equations of motion for the order parameter and perhaps any other conserved fields that reflect their intrinsic microscopic reversible dynamics as well as irreversible relaxation kinetics, the latter connected in thermal equilibrium with the noise strengths through Einstein relations or FDTs. Generally the various possible mode couplings of the order parameter to additional conserved, and consequently diffusively slow modes leads to a splitting of the static into several dynamic universality classes [16,18,9].…”

Section: Langevin Dynamics and Gaussian Theorymentioning

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: Langevin Dynamics and Gaussian Theorymentioning

confidence: 99%

Renormalization Group: Applications in Statistical Physics

Täuber

2012

Nuclear Physics B - Proceedings Supplements

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“…The dynamical critical exponent z OP is calculated in field theory from the so-called ζ-function at the dynamical fixed point. The renormalization procedure, which removes singularities (for a general introduction see [11]), leads to a renormalized kinetic coefficient Γ in the equation of motion for the order parameter. From these renormalization factors, the ζ-functions are obtained and their values at the stable dynamic fixed point (characterized by a star) give the values of dynamical exponents.…”

Section: General Considerations On Dynamicsmentioning

confidence: 99%

On the universality class of a magnetic liquid in an external field

Folk¹,

Moser²

2010

Condens. Matter Phys.

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“…The renormalization group method (RG) for the study of phase transitions and critical phenomena [1][2][3] allows one to justify the critical scaling and gives a recipe for calculating critical exponents as expansions in a small parameter ε = (d c − d)/2, which is the deviation from the critical dimension d c = 4 . The calculation of the renormalization-group functions is the main technical problem.…”

Section: Introductionmentioning

confidence: 99%

Multi-Loop Calculations of Anomalous Exponents in the Models of Critical Dynamics

Adzhemyan

Dančo

Hnatič

et al. 2016

EPJ Web of Conferences

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Abstract. The Renormalization group method (RG) is applied to the investigation of the E model of critical dynamics, which describes the transition from the normal to the superfluid phase in He 4 . The technique "Sector decomposition" with R' operation is used for the calculation of the Feynman diagrams. The RG functions, critical exponents and critical dynamical exponent z, which determines the growth of the relaxation time near the critical point, have been calculated in the two-loop approximation in the framework of ε-expansion. The relevance of a fixed point for helium, where the dynamic scaling is weakly violated, is briefly discussed.

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Critical dynamics: a field-theoretical approach

Cited by 144 publications

References 289 publications

Renormalization Group: Applications in Statistical Physics

Renormalization Group: Applications in Statistical Physics

On the universality class of a magnetic liquid in an external field

Multi-Loop Calculations of Anomalous Exponents in the Models of Critical Dynamics

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