The students will learn the remarkable phenomena
occurring at phase transitions that are
universally applicable to a wide range of systems, and
simple and physically intuitive theory for
deriving these phenomena. The dialog
between experiment and theory, as well as the
rich confluence of the
intuitive, phenomenological, approximate, rigorous, and
numerical approaches, will be
illustrated: Introduction: phase diagrams, thermodynamic
limit, critical phenomena, universality. Classical
theories: naive mean-field, constructive
mean-field, Landau theories; Ginzburg criterion. Ising
models and exact results: one dimension; two
dimensions; duality; global phase diagrams. Scaling
theory of Kadanoff. Exact renormalization-group treatments
in one dimension. Approximate renormalization-group
treatments in two dimensions. Thermodynamic
functions and first-order phase
transitions. Momentum-space renormalization
group: Gaussian model, Landau-Wilson
model, epsilon-expansion. Variational renormalization
group; Migdal-Kadanoff transformations.
Hierarchical lattices. Dynamics: stochastic
models; detailed balance; dynamic universality
classes. Superfluidity. Blume-Emery-Griffiths model. Global
multicritical phenomena. Surface systems. q-state
Potts and Potts-lattice-gas models. Exact critical
and tricritical exponents. Helicity and reentrance. Chaotic
renormalization groups and spin-glass
order. Order under frozen disorder and
frustration. Scale-free and small-world networks. Connection
between geometric and thermal properties.
Neural networks, simulated
annealing, coding-decoding, using phase transition
models. Renormalization-group theory of quantum
spin and electronic conduction models. High
Tc superconductivity. Electron-exchange
induced antiferromagnetism. Reverse
impurity effects on antiferromagnetism and
superconductivity.
|