Random field Ising model with conserved kinetics: Super-universality violation, logarithmic growth law and the generalized Tomita sum rule

We perform comprehensive Monte Carlo (MC) simulations to study ordering dynamics in the random field Ising model with conserved order parameter (C-RFIM) in $d=2,3$. The observations from this study are: a) For a fixed value of the disorder Δ, the correlation function $C(r,t;\Delta )$ exhibits dynamical scaling. b) The scaling function is not robust with respect to Δ, i.e., super-universality (SU) is violated by $C(r,t;\Delta )$. c) At early times, the domains follow the algebraic growth with a disorder-dependent exponent: $L(t,\Delta )\sim t^{1/\overline{z}\left(\Delta \right)}$. At late times, there is a crossover to logarithmic growth: $L(t,\Delta )\sim (\ln t{)}^{1/\phi }$, where φ is a disorder-independent exponent. d) The small-r behavior of the correlation function exhibits a cusp singularity: $1-C\left(r\right)\sim r^{\alpha \left(\Delta \right)}$, where α is the cusp exponent signifying rough fractal interfaces. e) The corresponding structure factor exhibits a non-Porod tail: $S(k,t;\Delta )\sim k^{-(d+\alpha )}$, and obeys a generalized Tomita sum rule ${\int }_0^{\infty }dp{p}^{1-\alpha }\left[p^{d+\alpha }f\right(p)-C]=0$, where f(p) is the appropriate scaling function, and $C$ is a constant. (letter)