Heriot-Watt Mathematics Report Series
HWM00-8, 17 Apr 2000
Slow dynamics of Ising models with energy barriers
A Lipowski, D Johnston and D Espriu
Abstract
Using Monte Carlo simulations we study the dynamics of three-dimensional
Ising models with
nearest-, next-nearest-, and four-spin (plaquette) interactions.
During coarsening, such models develop growing energy barriers, which leads at
low temperature to very slow dynamics.
As already reported, the model with only the plaquette interaction exhibits
some of the features characteristic for ordinary glasses:
a strong metastability of the supercooled liquid, a weak increase of the
characteristic length under cooling, a stretched-exponential relaxation and
aging.
The addition of two-spin interactions, in general, destroys such a behaviour: the liquid
phase looses metastability and the slow-dynamics regime terminates much below
the melting transition, which is presumably related with a certain
corner-rounding transition.
However, for a certain choice of interaction constants, when the ground
state is strongly degenerate, our simulations suggest that the slow-dynamics
regime extends up to the melting transition.
The analysis of these models leads us to the conjecture that in the four-spin Ising
model domain walls loose their tension at the glassy transition and they are basically tensionless in the glassy phase.
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Publication
A Lipowski, D A Johnston, D Espriu
, Slow dynamics of Ising models with energy barriers, Phys Rev E, 62, 3404-3410, (2000).
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