Aging dynamics and the topology of inhomogenous networks

Details Aging dynamics and the topology of inhomogenous networks Aging dynamics and the topology of inhomogenous networks

2006-06-14

arxiv.org/abs/cond-mat/0606367v1

Physical Review Letters 96, 235701 (2006)

Physics

Condensed Matter

Statistical Mechanics

LateX file, 4 eps figures

Scientific paper

10.1103/PhysRevLett.96.235701

We study phase ordering on networks and we establish a relation between the exponent $a_\chi$ of the aging part of the integrated autoresponse function $\chi_{ag}$ and the topology of the underlying structures. We show that $a_\chi >0$ in full generality on networks which are above the lower critical dimension $d_L$, i.e. where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with $T_c = 0$, which are at the lower critical dimension $d_L$, we show that $a_\chi$ 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 $d_L$, and for other networks, showing that the value of $a_\chi $ changes according to our hypothesis. For $O({\cal N})$ models we find that the same picture holds in the large-${\cal N}$ limit and that $a_\chi$ only depends on the spectral dimension of the network.

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