Critical Phenomena and Field Theory

Catalog description

Critical phenomena using field theoretical and renormalization group techni- ques; solvable statistical models and conformal field study; fluctuations and random processes. PHYS 518 Critical Phenomena and Field Theory (3) The application of field theoretical methods, in particular, the renormalization group approach, has profoundly influenced our understanding of the physics of continuous phase transitions. In particular, they reveal the origin of universality between seemingly unrelated phase transitions, and the reason for the failure of the Landau Ginzburg theory close to the critical point. This course will begin with the concepts of the order parameter and spontaneous symmetry breaking, and the shortcomings of the Landau Ginzburg theory that neglects fluctuations of the order parameter. Subsequently, we will introduce field theoretical techniques and Feynman diagrams, and the basic foundations of the renormalization group method for integrating out rapidly fluctuating modes of the order parameter. These concepts will be applied to various classes of phase transitions, including the Heisenberg ferromagnet, nonlinear sigma model, and the Kosterlitz-Thouless model. Epsilon expansion will be performed in detail starting from both four and two dimensions, and a connection will be made to experiments, such as superfluid transition in thin helium films. No prior knowledge of field theory is required. The course grade will be based upon homework assignments and a term paper.