Noise-driven dynamic phase transition in a one-dimensional Ising-like model
Abstract
The dynamical evolution of a recently introduced one-dimensional model [S. Biswas and P. Sen, Phys. Rev. E 80, 027101 (2009)] (henceforth, referred to as model I), has been made stochastic by introducing a parameter β such that β=0 corresponds to the Ising model and β→∞ to the original model I. The equilibrium behavior for any value of β is identical: a homogeneous state. We argue, from the behavior of the dynamical exponent z , that for any β≠0 , the system belongs to the dynamical class of model I indicating a dynamic phase transition at β=0 . On the other hand, the persistence probabilities in a system of L spins saturate at a value Psat(β,L)=(β/L)αf(β) , where α remains constant for all β≠0 supporting the existence of the dynamic phase transition at β=0 . The scaling function f(β) shows a crossover behavior with f(β)=constant for β≪1 and f(β)∝β-α for β≫1 .
- Publication:
-
Physical Review E
- Pub Date:
- March 2010
- DOI:
- 10.1103/PhysRevE.81.032103
- arXiv:
- arXiv:0912.2848
- Bibcode:
- 2010PhRvE..81c2103S
- Keywords:
-
- 05.40.Ca;
- 02.50.Ey;
- 03.65.Vf;
- 74.40.Gh;
- Noise;
- Stochastic processes;
- Phases: geometric;
- dynamic or topological;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 4 pages, 5 figures, accepted version in Physical Review E