Glassy dynamics and aging in an exactly solvable spin model

Details Glassy dynamics and aging in an exactly solvable spin model Glassy dynamics and aging in an exactly solvable spin model

1997-07-25

arxiv.org/abs/cond-mat/9707273v2

Phys. Rev. E 60, 5068-5072 (1999)

Physics

Condensed Matter

Statistical Mechanics

16 pages, 4 postscript figures, typeset in LaTeX using the RevTeX macro package

Scientific paper

10.1103/PhysRevE.60.5068

We introduce a simple two-dimensional spin model with short-range interactions which shows glassy behavior despite a Hamiltonian which is completely homogeneous and possesses no randomness. We solve exactly for both the static partition function of the model and the distribution of energy barriers, giving us the equilibration time-scales at low temperature. Simulations of instantaneous quenches and of annealing of the model are in good agreement with the analytic calculations. We also measure the two-time spin correlation as a function of waiting time, and show that the model has aging behavior consistent with the distribution of barrier heights. The model appears to have no sharp glass transition. Instead, it falls out of equilibrium at a temperature which decreases logarithmically as a function of the cooling time.

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