Lyapunov spectral analysis of a nonequilibrium Ising-like transition

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 ξ_δ, are insensitive to the onset of long-range ferromagnetic order. In particular, the dimension correlation length ξ_δ 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 g 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 ξ_δ are approximately equal, with both varying linearly with the radius of the lattice coupling.