Restricted equilibrium ensembles: Exact equation of state of a model glass
Department of Theoretical Physics, Tata Institute of Fundamental Research - Homi Bhabha Road, Mumbai-400005, India
2 Departments of Mathematics and Physics, Rutgers University - Piscataway, NJ 08854, USA
Accepted: 11 October 2010
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 the 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.
PACS: 05.70.Ce – Thermodynamic functions and equations of state / 64.60.My – Metastable phases / 02.50.Ga – Markov processes
© EPLA, 2010