Constrained spin dynamics description of random walks on hierarchical scale-free networks
| dc.creator | Noh, Jae Dong | |
| dc.creator | Rieger, Heiko | |
| dc.date | 2003-10-15 | |
| dc.date | 2004-04-10 | |
| dc.date.accessioned | 2026-07-07T02:54:12Z | |
| dc.date.available | 2026-07-07T02:54:12Z | |
| dc.description | We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule, which allows an analytic approach. We show analytically that the characteristic relaxation time scale grows algebraically with the total number of nodes $N$ as $T \sim N^z$. From a scaling argument, we also show the power-law decay of the autocorrelation function $C_{\bfsigma}(t)\sim t^{-α}$, which is the probability to find the Ising spins in the initial state ${\bfsigma}$ after $t$ time steps, with the state-dependent non-universal exponent $α$. It turns out that the power-law scaling behavior has its origin in an quasi-ultrametric structure of the configuration space. | |
| dc.description | 9 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0310344 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0310344 | |
| dc.identifier | Phys. Rev. E 69, 036111 (2004) | |
| dc.identifier | doi:10.1103/PhysRevE.69.036111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/22450 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Constrained spin dynamics description of random walks on hierarchical scale-free networks | |
| dc.type | text |