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.
|