Universal persistence exponent in transition to antiferromagnetic order in coupled logistic maps

作者：Gade Prashant M^*; Sahasrabudhe G G

来源：Physical Review E, 2013, 87(5): 052905.

DOI：10.1103/PhysRevE.87.052905

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(star) = 1 - 1/mu. 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.

• 出版日期2013-5-10