Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics
arXiv:1011.2225 · doi:10.1088/1742-5468/2011/05/P05017
Abstract
We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.
v2: Extensively modified to discuss both high temperature (non-symmetric) and low temperature (symmetric) renormalization group fixed points. Now 16 pages with 1 figure. v1: 13 pages
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Cited by in corpus (5)
- Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
- Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses
- Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables
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