# Christian Borgs

## University of Leipzig, Visiting AT&T

- DIMACS Center - Rutgers University
- CoRE Building Lecture Hall - Busch Campus
- Piscataway, New Jersey
- Friday October 4, 1996 at 11:30am-12:30pm

## "Birth of a Discontinuity: Finite-Size Scaling in Magnetic Systems and Lattice Gases,"

### Abstract:

A fundamental question in the study of phase transitions is the question
of finite-size scaling: How does thermodynamic behavior emerge from the
behavior of large, finite systems? In these two lectures, we address this
question in systems with both discontinuous and continuous phase transitions.
We review the necessary prerequisites from statistical mechanics.
Lecture 1 (joint work with J. Imbrie and R. Kotecky):
Here we study finite-size scaling in magnetic systems and lattice gases with
discontinous phase transitions. These systems are characterized by a jump
in an (infinite-volume) order parameter which is smoothed in finite volumes.
Using so-called cluster expansion methods, we study the the scaling form of
the cross-over from the smooth behavior of finite systems to the discontinuity
in the macroscopic system. We show that this scaling function is independent
of the details of the model (universality).

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Document last modified on September 27, 1996