Module description
This module will be taught jointly with the Department of Physics at Cardiff and Swansea, using the University of Wales video network. It consists of three blocks of lectures covering different applications of statistical physics:
(a) phase transitional and critical phenomena (Swansea)
(b) astrophysical applications (Cardiff)
(c) Information Theory (Aberystwyth)

Learning outcomes
After taking this module students should be able to:

• appreciate the factors determining phase transitions.
• understand the application of statistics in astrophysics.
• understand the concept of information and the link with Statistical Mechanics.

Additional learning activities
Example classes

Outline syllabus
Phase Transitions and Critical Phenomena : phase equilibrium conditions; Clausius-Clapeyron equation; distinction between 1st and 2nd order transitions, Ehrenfest criterion; notion of order parameter, symmetry breaking.

Examples: liquid vapour critical point, ferromagnetism and the Curie point, superconducting transition, Coulomb-Higgs transition and quark/hadron transition in the early universe.

Phenomenology of 2nd order transitions: non-analytic behaviour of order parameter near criticality, divergence of susceptibility/compressibility, critical opalescence.

Example: van der Waal's equation of state for a real gas.

The Ising Model: simple model for ferromagnetism, partition function, free energy, correlation functions, magnetism, susceptibility as derivatives of free energy wrt magnetic field, Curie-Weiss molecular field theory for critical properties.

Concept of divergent correlation length as T tends to Tc, universality, Landau-Ginsberg Theory and extension to 1st-order transitions.

Role of fluctuations: comparison of M.F.T. with actual exponents from exact solutions, simulations, measurements, renormalisation group approach - block spinning by decimation, phase transition corresponding to the fixed point and an improved estimate of exponents.

Degenerate stars, correlation functions in astronomy, statistics of stellar dynamics.

Information - the relation to probability; the message - the bit; message transmission - source, channel, destination; channel capacity - noise and bandwidth; entropy and information rate; coding; mutual information; the binary symmetric channel (BSC); coding for a BSC; Shannon's theorem; the relationship between Information Theory and Statistical Mechanics, information in a spectrum.