Long time limit of equilibrium glassy dynamics and replica calculation

Details Long time limit of equilibrium glassy dynamics and replica calculation Long time limit of equilibrium glassy dynamics and replica calculation

2007-10-02

arxiv.org/abs/0710.0601v4

Nuclear Physics B 796 [FS], 425-456 (2008)

Physics

Condensed Matter

Statistical Mechanics

25 pages, 12 Figures, RevTeX. Corrected misprints. Published version

Scientific paper

10.1016/j.nuclphysb.2007.11.039

It is shown that the limit $t-t'\to\infty$ of the equilibrium dynamic self-energy can be computed from the $n\to 1$ limit of the static self-energy of a $n$-times replicated system with one step replica symmetry breaking structure. It is also shown that the Dyson equation of the replicated system leads in the $n\to 1$ limit to the bifurcation equation for the glass ergodicity breaking parameter computed from dynamics. The equivalence of the replica formalism to the long time limit of the equilibrium relaxation dynamics is proved to all orders in perturbation for a scalar theory.

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