Schedule
Prerequisite
Course Outline
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Long-range order, symmetry and hydrodynamical modes;
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Phase transitions, mean field theory;
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Continuous and discontinuous phase transitions, the role of symmetry;
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Critical phenomena, scaling transformation, universality;
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Renormalization group, statistical field theory;
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Wilson-Fisher fix point near d = 4, calculation of critical exponents;
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Exactly solvable models: Ising, Potts, duality transformation;
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Topological transitions, vortices in the XY model, Kosterlitz-Thouless RG theory;
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XY and solid-on-solid duality, vortex melting of 2D crystals;
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Lower critical dimension, nonlinear sigma model;
and, if time permits,
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Critical dynamics, scaling theory;
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Field-theoretic description of localization;
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Conformal invariance and Conformal Field Theory in Statistical Mechanics.
Recommended Texts
Ma, S-K. Modern Theory of Critical Phenomena. The Bejamin/Cummings Publishing Co., 1976.
Amit, D. J. Field Theory, Renormalization Group, and Critical Phenomena. World Scientific, 1984.
Itzykson, C., and J-M Drouffe. Statistical Field Theory. Vol. 1, 2. Cambridge University Press, 1991.
Grading
Problem Sets 33.3%
Final Exam 33.3%
Term Paper 33.3%