Height-difference correlation function of the quenched Mullins-Herring equation

초록

We consider a discrete surface growth model following the quenched Mullins-Herring (qMH) equation with an external driving force. At the critical force, F,, the surface width W shows a scaling behavior W-2(t, L) similar to L(2 alpha)f(t/L-z) with alpha approximate to 1.35 and z approximate to 1.60, where L and t are the system size and time, respectively. However, the height-difference correlation function G has an unusual scaling behavior G(r,t) similar to r(2 alpha') g(r/t(1/z')) with different anomalous exponents alpha' approximate to 1.683 and z' approximate to 1.994. The correlation length xi grows as t(1/z') and becomes saturated with L-omega, where omega is the window exponent satisfying omega = alpha/alpha' = z/z' approximate to 0.802.