Journal
PHYSICAL REVIEW E
Volume 69, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.69.036111
Keywords
-
Categories
Ask authors/readers for more resources
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 Tsimilar toN(z). From a scaling argument, we also show the power-law decay of the autocorrelation function C-sigma(t)similar tot(-alpha), which is the probability to find the Ising spins in the initial state sigma after t time steps, with the state-dependent nonuniversal exponent alpha. It turns out that the power-law scaling behavior has its origin in a quasiultrametric structure of the configuration space.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available