Pradipta Kumar Mandal and Debnarayan Jana 2009 J. Phys. A: Math. Theor. 42 485004 doi:10.1088/1751-8113/42/48/485004
Pradipta Kumar Mandal and Debnarayan Jana
Show affiliationsWe demonstrate the non-universal behavior of finite-size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in a generalized point of view. In particular, we show the violation of the universal nature of the scaling function corresponding to the height fluctuation in (1+1) dimension. The second-order moment of the height fluctuation shows three distinct crossover regions separated by two crossover timescales namely, t×1 and t×2. Each regime has different scaling properties. The overall scaling behavior is postulated with a new scaling relation represented as the linear sum of two scaling functions valid for each scaling regime. Besides, we note the dependence of the roughness exponents on the finite size of the system. The roughness exponents corresponding to the rough surface is compared with the growth rate or the velocity of the surface.
68.35.Ct Interface structure and roughness
68.55.A- Nucleation and growth
61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates)
64.60.A- Specific approaches applied to studies of phase transitions
82C26 Dynamic and nonequilibrium phase transitions (general)
82C24 Interface problems; diffusion-limited aggregation
82C80 Numerical methods (Monte Carlo, series resummation, etc.)
65F35 Matrix norms, conditioning, scaling (See also 15A12, 15A60)
Issue 48 (4 December 2009)
Received 19 June 2009, in final form 9 October 2009
Published 13 November 2009
Pradipta Kumar Mandal and Debnarayan Jana 2009 J. Phys. A: Math. Theor. 42 485004
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