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A Monte Carlo method is used in order to simulate the competition between the molecular relaxation and crystallization times in the formation of a glass. The results show that nucleation is avoided during supercooling and produce self-organization in the sense of the rigidity theory, where the number of geometrical constraints due to bonding and excluded volume are compared with the degress of freedom available to the system. Following this idea, glass transitions were obtained by producing self-organization, and in the case of geometrical frustration, self-organization is naturally observed.
Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by appl
In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we fi
In this paper, we will investigate critical phenomena by considering a model spin-glass on scale-free networks. For this purpose, we consider the Ghatak-Sherrington (GS) model, a spin-1 spin-glass model with a crystal field, instead of the usual Isin
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter i
We show in numerical simulations that a system of two coupled replicas of a binary mixture of hard spheres undergoes a phase transition in equilibrium at a density slightly smaller than the glass transition density for an unreplicated system. This re