scholarly journals Real-space Renormalization Group analysis of a non-mean-field spin-glass

2011 ◽  
Vol 95 (4) ◽  
pp. 47014 ◽  
Author(s):  
M. Castellana
Keyword(s):  
Renormalization Group ◽  
Spin Glass ◽  
Group Analysis ◽  
Mean Field ◽  
Real Space ◽  
Renormalization Group Analysis ◽  
Real Space Renormalization Group

scholarly journals Real space renormalization group theory of disordered models of glasses

2017 ◽  
Vol 114 (13) ◽  
pp. 3328-3333 ◽  
Author(s):  
Maria Chiara Angelini ◽  
Giulio Biroli
Keyword(s):  
Renormalization Group ◽  
Glass Transition ◽  
Fixed Points ◽  
Degrees Of Freedom ◽  
Group Analysis ◽  
Real Space ◽  
Energy Scale ◽  
Renormalization Group Analysis ◽  
Real Space Renormalization Group ◽  
Disordered Models

We develop a real space renormalization group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their renormalization group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition.

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