# DIMACS Focus on Discrete Probability Seminar

## Title:

Some Non-Tribial Exponents in The one-Dimensional Ising Model

## Speaker:

- B.Derrida
- Laboratoire de Physique Statistique

## Place:

- DIMACS Center, CoRE Building, Seminar Room 431
- Busch Campus, Rutgers University.

## Time:

- 3:30 - 4:30 PM
- Wednesday, November 6, 1996

**Abstract:**
Exponents appearing in the zero temperature dynamics of one dimensional
spin models.

One of the simplest problems of stochastic automata is the Glauber dynamics
of ferromagnetic spin models such as Ising or Potts models. At zero
temperature, if the initial condition is random, one observes a pattern of
growing domains with a characteristic size which increases with time like
$t^{1/2}$. In this self similar regime, one can show that the fraction of
spins which never move up to time $t$ decreases like $t^{-\theta}$ where the
exponent $\theta$ is non trivial and depends both on the number of states of
the Potts model and on the dimension of space. This exponent can be calculated
exactly in one dimension, confirming the values previously determined by
numerical methods. Similar non-trivial exponents are also present in even
simpler models of coarsening, where the dynamical rule is deterministic.

Document last modified on November 1, 1996