- 11-63 Jean-Pierre Eckmann, Maher Younan
- Decay of Correlations in a Topological Glass
Apr 20, 11
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Abstract. In this paper we continue the study of a topological glassy system. 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 other numbers of neighbors are supposed to be
positive. The dynamics is that of flipping the diagonal between two adjacent triangles, with a temperature
dependent probability. We consider the system at very low temperatures.
We concentrate on several new aspects of this model: Starting from a detailed description of the stationary
state, we conclude that pairs of defects (nodes with the wrong degree) move with very high mobility
along 1-dimensional paths. As they wander around, they encounter single defects, which they then move
sideways with a geometrically defined probability. This induces a diffusive motion of the single defects.
If they meet, they annihilate, lowering the energy of the system. We both estimate the decay of energy to
equilibrium, as well as the correlations. In particular, we find a decay like t^−0.4.