Jean-Pierre Eckmann
A Topological Glass
(2329K, postscript)
ABSTRACT. We propose and study a model with glassy behavior. The state space
of the model is given by all triangulations of a sphere with $n$
nodes, half of which are red and half are blue. Red nodes want to
have 5 neighbors while blue ones want 7. Energies of nodes with
different numbers of neighbors are supposed to be positive.
The dynamics is that of
flipping the diagonal of two adjacent triangles, with a temperature
dependent probability. We show that this system has an approach to a
steady state which is exponentially slow, and show that the
stationary state is unordered. We also study the local energy
landscape and show that it has the hierarchical structure known from
spin glasses. Finally, we show that the evolution can be described as that of
a rarefied gas with spontaneous generation of particles and annihilating collisions.