Phase Transitions

August 21 to August 25, 2006

at the

American Institute of Mathematics, San Jose, California

organized by

Persi Diaconis, Daniel Fisher, Cris Moore, and Charles Radin

Original Announcement

This workshop will be devoted to the study of phase transitions in several traditionally separate subjects.

Phase transitions have been an important part of statistical mechanics for many years. More recently phase transitions have become a hot topic in computer science (study of 3-satisfiability), combinatorics (birth of the giant component for various random graph models) and probability theory (cutoff phenomena for markov chains). We propose to bring together experts within each area to present the various intuitions, motivations, canonical examples and conceptual techniques of their areas, the hope being to come to agreement on a few key definitions, and perhaps thereby to bring fresh ideas to bear on open problems.

Examples of topics for discussion/open problems:

  1. Various definitions of phase transitions.
  2. Proof of a solid/fluid phase transition, for instance in the hard sphere or hard disk model, or related nonequilibrium models of granular materials.
  3. Proof of a rigorous connection between the birth of a giant component in random graph theory, and of the cutoff phenomenon for markov chains.
  4. Proof of a sharp phase transition for the algorithmic K-SAT problem, for K > 2.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

You can download slides from the talks by Tom Witten, Andrea Liu, Susan Coppersmith, and Sidney Nagel.

A definition of thermodynamic phases and phase transitions by Michael Fisher and Charles Radin.