Emergence of continuously varying critical exponents in coupled map lattice as an effect of quenched disorder

Abstract

The transition to an absorbing phase in a spatiotemporal system is a well-investigated nonequilibrium dynamic transition. The absorbing phase transitions fall into a few universality classes, defined by the critical exponents observed at the critical point. We present a coupled map lattice (CML) model with quenched disorder in the couplings. In this model, spatial disorders are introduced in the form of asymmetric coupling with a larger coupling ($p$) to a neighbor on the right and a smaller coupling ($1-p$) to the neighbor on the left, for $0\le p\le 0.5$. For $p=0$, the system belongs to the directed percolation universality class. For $p>0$, we observe continuously changing critical exponents at the critical point. The order parameter is the fraction of turbulent sites $m(t)$. %sites that are not in the laminar region. We observe a power-law decay, $m(t)\sim t^{-\delta }$, at the critical point ${\epsilon }_c$, where $\epsilon$ is the diffusive coupling parameter. These exponents change continuously and do not match any known universality class in any limit. This could be related to changes in the eigenvalue spectrum of the connectivity matrix as the disorder is introduced.

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