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Statistical mechanics and disordered systems — Università Tor Vergata, 2025

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Plan of the lectures:

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• Lecture 1 (May 26):
  General introduction to disordered systems, first examples (Ising model, random interfaces).
  • Recipe for disordered systems, homogeneous vs. disordered Gibbs measures;
  • Ising model: with homogeneous interactions (phase transition for the magnetization), with a random external field (Imry-Ma argument and mathematical results);
    References: Friedli-Velenik's book, Chapter 3; Dario-Peled's lecture notes (in construction).
  • Random interfaces: homogeneous model and delocalization/localization of the interface, with a random external field (Imry-Ma argument and mathematical results);
    References: Velenik's survey on random interfaces; Dario-Harel-Peled's article.

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• Lecture 2 (June 3):
  Homogeneous and disordered pinning model

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• Lecture 3 (June 5):
  Irrelevant vs relevant disorder for the pinning model

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• Lecture 4 (June 9):
  The directed polymer model, first properties, phase transition

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• Lecture 5 (June 12):
  Weak disorder for the directed polymer model

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• Lecture 6 (June 16):
  Strong disorder for the directed polymer model

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• Lecture 7 (June 19):
  Scaling limit of the directed polymer model, in relation with the Stochastic Heat Equation