New approach to study mobility in the vicinity of dynamical arrest; exact application to a kinetically constrained modelP. De Gregorio1, 2, A. Lawlor1 and K. A. Dawson1
1 Irish Centre for Colloid Science and Biomaterials, School of Chemistry and Chemical Biology, University College Dublin - Belfield, Dublin 4, Ireland
2 Dipartimento di Fisica, Università di Roma La Sapienza - I-00185 Roma, Italy
received 2 November 2005; accepted in final form 28 February 2006
published online 22 March 2006
We introduce a new method to describe systems in the vicinity of dynamical arrest. This involves a map that transforms mobile systems at one length scale to mobile systems at a longer length. This map is capable of capturing the singular behavior accrued across very large length scales, and provides a direct route to the dynamical correlation length and other related quantities. The ideas are immediately applicable in two spatial dimensions, and have been applied to a modified Kob-Andersen-type model. For such systems the map may be derived in an exact form, and readily solved numerically. We obtain the asymptotic behavior across the whole physical domain of interest in dynamical arrest.
64.70.Pf - Glass transitions.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
64.60.Ak - Renormalization-group, fractal, and percolation studies of phase transitions.
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