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arXiv · 1008.3011

Restricted equilibrium ensembles: Exact equation of state of a model glass

Deepak Dhar·Joel L. Lebowitz
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Abstract

We investigate the thermodynamic properties of a toy model of glasses: a hard-core lattice gas with nearest neighbor interaction in one dimension. The time-evolution is Markovian, with nearest-neighbor and next-nearest neighbor hoppings, and the transition rates are assumed to satisfy detailed balance condition, but the system is non-ergodic below a glass temperature. Below this temperature, the system is in restricted thermal equilibrium, where both the number of sectors, and the number of accessible states within a sector grow exponentially with the size of the system. Using partition functions that sum only over dynamically accessible states within a sector, and then taking a quenched average over the sectors, we determine the exact equation of state of this system.

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Deepak Dhar, Joel L. Lebowitz. 2010-08-18. Restricted equilibrium ensembles: Exact equation of state of a model glass. https://doi.org/10.1209/0295-5075%2F92%2F20008

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