Path integral methods for the dynamics of stochastic and disordered systems

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 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.

review article, 37 pages

References in corpus (5)

• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Dynamical TAP equations for non-equilibrium Ising spin glasses
• Extended Plefka Expansion for Stochastic Dynamics
• Variational perturbation and extended Plefka approaches to dynamics on random networks: the case of the kinetic Ising model
• BEST statistics of Markovian fluxes: a tale of Eulerian tours and Fermionic ghosts

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