Breaking of ergodicity and long relaxation times in systems with long-range interactions

Details Breaking of ergodicity and long relaxation times in systems with long-range interactions Breaking of ergodicity and long relaxation times in systems with long-range interactions

2005-08-25

arxiv.org/abs/cond-mat/0508604v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.95.240604

The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long range interactions and are expected to be valid even when the interaction is slowly decaying with distance.

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