Lyapunov spectral analysis of a nonequilibrium Ising-like transition

Journal Article

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length ξδ, are insensitive to the onset of long-range ferromagnetic order In particular the dimension correlation length ξδ remains finite and of order 1 lattice spacing while the two-point correlation length diverges to infinity. As a function of lattice coupling constant g and for certain lattice maps, the Lyapunov dimension density and other dynamical order parameters go through a minimum. The occurrence of this minimum as a function of , depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry, on the lattice dimensionality, or on the position of the Ising-like transition. In one-space dimension, the spatial correlation length associated with magnitude fluctuations and the length ξδ are approximately equal, with both varying linearly with the radius of the lattice coupling.

Duke Authors

Cited Authors

  • O'Hern, CS; Egolf, DA; Greenside, HS

Published Date

  • 1996

Published In

  • Physical Review E Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volume / Issue

  • 53 / 4 SUPPL. A

Start / End Page

  • 3374 - 3386