Physics and Astronomy Colloquium
Tuesday, January 22, 2002
4:10 p.m., Room 118 Physics-Astronomy Building
Refreshments at 3:45 p.m. outside Room 224
(Students are welcome to meet with Dr. Mattis in Room 224
from 3:15-3:45 on Tuesday)
Daniel C. Mattis
University of Utah
THE USES OF THE TRANSFER MATRIX IN STATISTICAL PHYSICS
Abstract:
This talk seeks to clarify an approach to mathematical statistical physics
that has been successful in numerous applications. It will be of interest to
students in many areas of theoretical physics, although presented at a level
accessible to beginning graduate students.
Using simple concepts, we make use of translational invariance to
reformulate models of magnetism, spin glasses, and the "zipper model"
(cracks in crystals) as eigenvalue problems.
We illustrate by applying the transfer matrix to some extremely simple
homogeneous materials and the hyper-transfer matrix to the simplest
possible disordered media.
We examine and expose some of the special tricks used to solve the
eigenvalue problems that are generated.