Faculty of Science

Objectives

To explore different approaches to critical phenomena and phase transitions in condensed matter systems, with emphasis on the Mean-Field and the renormalization-group theory based on scaling considerations.

Contents

Brief review of the formalism of statistical mechanics: partition functions and the connection with thermodynamics; Statistical mechanics of phase transitions in different systems, first-order and second order phase transitions, Mean-Field theory of phase transition, Landau theory, correlation functions, transfer matrix, free energy, role of fluctuations, the Ginzburg criteria; Examples: the one-dimensional Ising model, the SY and Heisenberg models; Critical phenomena: critical exponents and exponent inequalities, scaling and universality: Renormalization group theory: scaled variables, self-similarity, the flow equations and flow in parameter space.