Statistical Mechanics

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Main topics

Part (A)

Basic notions

• ensemble microcanonical, canonical and grancanonical
• Boltzamann, Bose and Fermi statistics
• quantum statistical mechanics

Phase Transition

• Ising model (Transfer matrix in 1D + field etc.)
• Weiss approach
• critical exponents
• variational principles and mean field
• infinite range model
• scaling relations, Widom hypothesis and its consequences
• finite-size scaling

Computational methods and off-equilibrium

• master equation
• Langevin approach
• importance sampling and Monte Carlo
• Simulated annealing
• reweighting techniques

Part (B)

Soft-condensed matter

• Statistical mechanics for polymers
• percolation theory