Physics 525, Fall 2009

ADVANCED STATISTICAL PHYSICS

Marcel den Nijs Office: PAB B429 Department of Physics University of Washington Seattle. dennijs@phys.washington.edu

OUTLINE:

This is the second quarter of the graduate statistical mechanics course, with as focus equilibrium and non-equilibrium phase transitions and scale invariant phenomena in general. The course will start with a general introduction to equilibrium critical phenomena, including how scale invariance and universality arise, and why Landau theory fails at criticality. This is followed by an introduction of scale invariance and renormalization theory from a geometric perspective, i.e., starting from fractal structures, accumulating into the real space renormalization method. Next we will discuss examples of two dimensional equilibrium critical phenomena, like: vortices in He films, crystalline surface roughening, Kosterlitz-Thouless phase transitions, the duality of many 2D equilibrium systems to Coulomb gases with logarithmic interactions, and the renormalization theory of the latter. In the last part of the course we can choose to cover the exact solution of the 2D Ising model, using the transfer matrix (path integral) and leading to the equivalence to one dimensional free fermion dynamics; and in general to Luttinger liquid theory and conformal invariance. Or we can choose to cover non-equilibrium statistical physics, in particular master equations describing interface phenomena like KPZ growth and population dynamics like directed percolation; followed maybe by a brief overview of self-organized critical phenomena.

TEXTBOOK:

We will not follow any text in a linear fashion. I will post lecture notes. These include detailed references to the literature. Some of my review papers and lectures at Winter/Summer Schools are available here. Recomended text books for this class include Equilibrium Statistical Physics by Plischke and Bergerson, and Quantum and Statistical field Theory by Le Ballac.