It is proposed that the dynamic heterogeneities of an amorphous material are strongly correlated with the spatial distribution of unconstrained degrees of freedom in the associated network of mechanical constraints. This latter distribution is shown to depend sensitively on whether or not overconstraints are permitted in the constraint network. When overconstraints are avoided, relaxation is achieved with few bond rearrangements and the susceptibility χ(4) increases monotonically with increasing constraint density, in contrast to the case of a random network. This behaviour is associated with the marginal stability of the isostatic rigid cluster as opposed to the more robust structures generated when redundant bonds are permitted.
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