Rostiashvili VG, Vilgis TA. Dynamics of structural models with a long-range interaction: glassy versus nonglassy behavior.
PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000;
62:1560-1576. [PMID:
11088618 DOI:
10.1103/physreve.62.1560]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2000] [Indexed: 05/23/2023]
Abstract
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 are considered: (i) the nondisordered 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 the GF the saddle-point treatment as well as the systematic 1/N expansion around it. We show that the nondisordered 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 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.
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