2016/04/20 by John A. Hertz, John A Hertz, Yasser Roudi +1 · 78 citations
Computer Science · Physics and Astronomy · #Formalism (music) #Ising model #Ising spin #Path integral formulation #Quantum Information and Cryptography #Quantum many-body systems #Spins #Stochastic dynamics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8121/50/3/033001
published in Journal of Physics A Mathematical and Theoretical 50(3), 033001 (Institute of Physics) · review article, 37 pages
arxiv created 2016/04/20 · openalex created_date 2016/06/24 · openalex publication_date 2016/12/12 · arxiv updated 2017/01/26 · openalex updated_date 2026/08/05
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.