Flux Lines, Superconductors, and Self-Avoiding Walks
Neal Madras
Department of Mathematics and Statistics, York University
Abstract
Flux lines of a magnetic field can be modeled as a collection of mutually avoiding self-avoiding walks passing through some region of
a lattice. I shall describe a statistical mechanical model of flux lines that can be analyzed rigorously using some combinatorial methods.
The physically most interesting version of the model exhibits three phases that correspond qualitatively to what has been observed in
"Type II" superconductors: a Meissner phase (in which the flux lines are expelled), a "frozen" phase (in which the flux lines form a lattice),
and an intermediate "flux liquid" phase.
This is joint work with Christian Borgs, Jennifer Chayes, and Christopher King.
