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Path integral methods for the dynamics of stochastic and disordered systems

Hertz, John A.; Roudi, Yasser; Sollich, Peter
Journal article, Peer reviewed
Published version
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URI
http://hdl.handle.net/11250/2496027
Date
2017
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  • Kavliinstitutt for nevrovitenskap [177]
  • Publikasjoner fra CRIStin - NTNU [20946]
Original version
Journal of Physics A: Mathematical and Theoretical. 2017, 50 (3), 1-47.   10.1088/1751-8121/50/3/033001
Abstract
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.
Publisher
IOP Publishing
Journal
Journal of Physics A: Mathematical and Theoretical

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