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Mathematical Physics by Michael Aizenman

Mathematical Physics by Michael Aizenman

Mathematical Physics by Michael Aizenman

The PDF covers the following topics related to Mathematical Physics : Introduction to statistical mechanics, Canonical Ensembles for the Lattice Gas, Configurations and ensembles, The equivalence principle, Generalizing Ensemble Analysis to Harder Cases, Concavity and the Legendre transform, Basic concavity results, Concave properties of the Legendre transform, Basic setup for statistical mechanics, Gibbs equilibrium measure, Introduction to the Ising model, Entropy, energy, and free energy, Large deviation theory, Free energy, Basic Properties, Convexity of the pressure and its implications, Large deviation principle for van Hove sequences, 1-D Ising model, Transfer matrix method, Markov chains, 7 2-D Ising model, Ihara graph zeta function, Gibbs states in the infinite volume limit, Conditional expectation, Symmetry and symmetry breaking, Phase transitions, Random field models, Proof of symmetry-breaking of continuous symmetries, The spin-wave perspective, Infrared bound, Reflection positivity.

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s76 Pages
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