Random Interactions

Power laws in space-time: Real and complex exponents, Self- organized criticality and Griffiths phase

by Dr. Prashant Gade (RMT Nagpur University)

Thursday, May 26, 2022 from to (Asia/Kolkata)
at A304 and Zoom
Power laws in space and time are obtained in a variety of systems. Self-organized criticality was an exotic explanation proposed by PerBak and coworkers. We present a dynamical model of evolution on lines of the Bak-Sneppen model in which a species that 'appears to be less fit' is punished instead of a 'least fit' species. The fitness is inferred from the dynamics of a coupled map lattice model. Some of the exponents obtained differ from the Bak-Sneppen model. Another (less exotic but more likely) route to power-laws in space has been quenched disorder and Griffiths phase. We study contact processes a) with unidirectional couplings b) with some sites evolving according to the rule in compact directed percolation class and the rest following the rule in directed percolation universality class. In the first case, we observe continuously varying complex exponents for order parameter decay (as a function of the parameter), i.e. power-laws superposed with log-periodic oscillations. This demonstrates the possibility of a 'complex Griffiths phase'. In another case, we observe complex persistence exponents which are continuously varying in the active phase. None of the systems has an underlying fractal or self-similar topology. We propose that effective fragmentation of lattice in dynamics leads to log-periodicity.

1) Maneesh Matte and PMG, Commun. Nonlin. Sci. Numer. Simul , 65, 91 (2018).
2) Priyanka Bhoyar and PMG, PRE, 103, 022115 (2021).
3) Priyanka Bhoyar and PMG, PRE, 101, 022128 (2020).