#
Phase Transitions

August 21 to August 25, 2006
at the

American Institute of Mathematics,
Palo Alto, 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:

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