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Aging dynamics and the topology of inhomogenous networks | | R. Burioni
; D. Cassi
; F. Corberi
; A. Vezzani
; | | Date: |
14 Jun 2006 | | Journal: | Physical Review Letters 96, 235701 (2006) | | Subject: | Statistical Mechanics | | Abstract: | 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. | | Source: | arXiv, cond-mat/0606367 | | Other source: | [GID 555765] pmid16803384 | | Services: | Forum | Review | PDF | Favorites | |
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