Towards a Theory of the Glass Crossover
Abstract
The standard field-theoretical procedure to study the effect of long wavelength fluctuations on a genuine second-order phase transition is applied to the Mode-Coupling-Theory (MCT) dynamical singularity at $T_c$ in the $\beta$ regime. Technically this is achieved by a dynamical field-theoretical decoration of MCT that can be studied by a loop expansion. An explicit computation shows that at all orders the leading contributions are the same of a dynamical stochastic glassy equation, {\it i.e} an extension of the standard MCT equation for the critical correlator with local random fluctuations of the separation parameter. It is suggested that the equation is an essential ingredient in the process that turns the singularity at $T_c$ into a dynamical crossover to activated dynamics.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.4303
- arXiv:
- arXiv:1307.4303
- Bibcode:
- 2013arXiv1307.4303R
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 7th IDMRCS