Aging dynamics and the topology of inhomogenous networks

We study phase ordering on networks and we establish a relation between the exponent a_ of the aging part of the integrated autoresponse function _ag and the topology of the underlying structures. We show that a_ > 0 in full generality on networks which are above the lower critical dimension dL, i.e., where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with Tc _ 0, which are at the lower critical dimension dL, we show that a_ is expected to vanish. We provide numerical results for the physically interesting case of the 2 _ d percolation cluster at or above the percolation threshold, i.e., at or above dL, and for other networks, showing that the value of a_ changes according to our hypothesis. For O_N_ models we find that the same picture holds in the large-N limit and that a_ only depends on the spectral dimension of the network.