Path integral methods for the dynamics of stochastic and disordered systems
Publikation: Bidrag til tidsskrift › Review › Forskning › fagfællebedømt
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Path integral methods for the dynamics of stochastic and disordered systems. / Hertz, John A.; Roudi, Yasser; Sollich, Peter.
I: Journal of Physics A: Mathematical and Theoretical, Bind 50, Nr. 3, 033001, 20.01.2017.Publikation: Bidrag til tidsskrift › Review › Forskning › fagfællebedømt
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TY - JOUR
T1 - Path integral methods for the dynamics of stochastic and disordered systems
AU - Hertz, John A.
AU - Roudi, Yasser
AU - Sollich, Peter
PY - 2017/1/20
Y1 - 2017/1/20
N2 - We review some of the techniques used to study the dynamics of disorderedsystems subject to both quenched and fast (thermal) noise. Starting from theMartin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism fora single variable stochastic dynamics, we provide a pedagogical survey of theperturbative, i.e. diagrammatic, approach to dynamics and how this formalismcan be used for studying soft spin models. We review the supersymmetricformulation of the Langevin dynamics of these models and discuss the physicalimplications of the supersymmetry. We also describe the key stepsinvolved in studying the disorder-averaged dynamics. Finally, we discuss thepath integral approach for the case of hard Ising spins and review some recentdevelopments in the dynamics of such kinetic Ising models.
AB - We review some of the techniques used to study the dynamics of disorderedsystems subject to both quenched and fast (thermal) noise. Starting from theMartin–Siggia–Rose/Janssen–De Dominicis–Peliti path integral formalism fora single variable stochastic dynamics, we provide a pedagogical survey of theperturbative, i.e. diagrammatic, approach to dynamics and how this formalismcan be used for studying soft spin models. We review the supersymmetricformulation of the Langevin dynamics of these models and discuss the physicalimplications of the supersymmetry. We also describe the key stepsinvolved in studying the disorder-averaged dynamics. Finally, we discuss thepath integral approach for the case of hard Ising spins and review some recentdevelopments in the dynamics of such kinetic Ising models.
KW - path integral methods
KW - disordered systems
KW - spin glasses
KW - dynamics
U2 - 10.1088/1751-8121/50/3/033001
DO - 10.1088/1751-8121/50/3/033001
M3 - Review
VL - 50
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 3
M1 - 033001
ER -
ID: 172472689