Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-03-28
Physics
Condensed Matter
Statistical Mechanics
to be published in Phys. Rev E
Scientific paper
10.1103/PhysRevE.62.1560
By making use of the Langevin dynamics and its generating functional (GF) formulation the influence of the long-range nature of the interaction on the tendency of the glass formation is systematically investigated. In doing so two types of models is considered: (i) the non-disordered model with a pure repulsive type of interaction and (ii) the model with a randomly distributed strength of interaction (a quenched disordered model). The long-ranged potential of interaction is scaled with a number of particles $N$ in such a way as to enable for GF the saddle-point treatment as well as the systematic 1/N - expansion around it. We show that the non-disordered model has no glass transition which is in line with the mean-field limit of the mode - coupling theory (MCT) predictions. On the other hand the model with a long-range interaction which above that has a quenched disorder leads to MC - equations which are generic for the $p$ - spin glass model and polymeric manifold in a random media.
Rostiashvili Vakhtang G.
Vilgis Thomas A.
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