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~$\xi_\delta$ are
insensitive to the onset of long-range ferromagnetic order. 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~$\xi_\delta$ are approximately equal, with both
varying linearly with the radius of the lattice coupling.
O'Hern, CS; Egolf, DA; Greenside, HS
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