title: Universal persistence exponent in transition to antiferromagnetic order in coupled logistic maps.
abstract: We study coupled logistic maps on a one-dimensional lattice. We coarse grain the system by labeling the local state + if the value of the variable is above the fixed point and - if the value is below the (nonzero) fixed point, x(*)=1-1/μ. We find that the system exhibits a transition from a global state, in which moving defects occur, to a global state, which is frozen in time (modulo-2). All such states display nonzero value of persistence. Besides, we also observe a state which displays long-range antiferromagnetic order. Onset of such a state is accompanied with a power-law behavior of persistence P(t) as a function of time at the critical line. Usually, persistence transitions show nonuniversal exponent. However, here persistence exponent for synchronous dynamics is 3/8 over the entire lower critical curve. This exponent is the same as one observed for asynchronous Glauber dynamics simulation of zero-temperature Ising model in one dimension. The expected value for synchronous dynamics is 3/4. We present a plausible argument for this scaling.
authors.affiliation: PG Department of Physics, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, India. prashant.m.gade@gmail.com
authors.forename: Prashant M
authors.initials: PM
authors.lastname: Gade
authors.forename: G G
authors.initials: GG
authors.lastname: Sahasrabudhe
mesh_terms: D003198:Computer Simulation; D060526:Magnetic Fields; D015233:Models, Statistical; D017711:Nonlinear Dynamics