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The kinetic Ising model on a n-isotopic chain is considered in the frameworkof Glauber dynamics. The chain is composed of N segments with n sites, each oneoccupied by a different isotope. Due to the isotopic mass difference, the nspins in each segment have different relaxation times in the absence of theinteractions, and consequently the dynamics of the system is governed bymultiple relaxation mechanisms. The solution is obtained in closed form forarbitrary n, by reducing the problem to a set of n coupled equations, and it isshown rigorously that the critical exponent z is equal to 2. Explicit resultsare obtained numerically for any temperature and it is also shown that thedynamic susceptibility satisfies the new scaling (Nagel scaling) proposed forglass-forming liquids. This is in agreement with our recent results (L. L.Goncalves, M. Lopez de Haro, J. Taguena-Martinez and R. B. Stinchcombe, Phys.Rev. Lett. 84, 1507 (2000)), which relate this new scaling function to multiplerelaxation processes.Comment: 4 pages, 2 figures, presented at Ising Centennial Colloquium, to be  published in the Proceedings (Brazilian Journal of Physics.

Nagel scaling and relaxation in the kinetic Ising model on an n-isotopic chain