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Kinetically Constrained Models

This book offers an in-depth review of kinetically constrained models (KCMs), a topic that lies at the crossroads of probability and statistical mechanics. KCMs have captivated physicists ever since their introduction in the 1980s. Their remarkable glassy behavior makes them an essential toy model f...

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Salvato in:
Dettagli Bibliografici
Autori principali: Hartarsky, Ivailo (Autore), Toninelli, Cristina (Autore)
Ente Autore: SpringerLink (Online service)
Natura: Elettronico eBook
Lingua:inglese
Pubblicazione: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Edizione:1st ed. 2025.
Serie:SpringerBriefs in Mathematical Physics, 53
Soggetti:
System theory.
Probabilities.
Mathematical physics.
Complex Systems.
Probability Theory.
Mathematical Physics.
Mathematical Methods in Physics.
Theoretical, Mathematical and Computational Physics.
Accesso online:https://doi.org/10.1007/978-3-031-93115-4
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Sommario:
  • Preface
  • The models
  • Setting and notation
  • The Markov processes: kinetically constrained spin models and kinetically constrained lattice gases
  • The most studied choices of constraints
  • Some useful classification: oriented/non–oriented models, cooperative/non–cooperative models
  • Motivations from physics
  • A crash course on liquid/glass and jamming transitions
  • The quest of the ideal glass transition: models on Bethe lattices and the spiral model
  • Kinetically Constrained Spin Models: the basic results
  • Ergodicity and connection with bootstrap percolation
  • Exponential convergence to equilibrium in L2
  • The failure of classic coercive inequalities (logarithmic and modified logarithmic Sobolev constant)
  • Persistence and exchange times
  • Scaling with density of the spectral gap: the case of Friedrickson-Andersen 1f model
  • Some open problems
  • Kinetically Constrained Spin Models on trees
  • A martingale technique to prove positivity of the spectral gap
  • Power law scaling at criticality
  • An open problem
  • The out of equilibrium regime
  • An easy perturbative result in one dimension
  • Oriented models: East and models on trees
  • Non cooperative models
  • Some open problems
  • Dynamical phase transition
  • Activity and its large deviations
  • The one dimensional case: finite size effects and surface tension
  • Open problems
  • The East model
  • Combinatorics
  • Spectral gap and mixing time
  • Time scale separation
  • Front motion and cut-off
  • Plateau behavior, aging and scaling limits
  • The generalized East process in higher dimensions
  • An open problem: Aldous Diaconis conjecture
  • Kinetically Constrained Lattice Gases
  • Ergodicity
  • Non cooperative models: spectral gap, log-Sobolev, tagged particle and hydrodynamic limit
  • Cooperative models: spectral gap and polynomial decay to equilibrium.

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