Erratum: Short-time scaling behavior of growing interfaces [Phys. Rev. E55, 668 (1997)]

Abstract

The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the "initial slip" behavior found in purely dissipative critical relaxation (model A). Unlike model A the initial slip exponent for the KPZ equation can be expressed by the dynamical exponent z. In 2+1 dimensions z is estimated from the short-time evolution of the correlation function for ballistic deposition and for the RSOS model.

Phenomenology of aging in the Kardar-Parisi-Zhang equation

“…The data are fully compatible with a numerical solution of the KPZ equation and directly test simple ageing (1) in the 1D KPZ class. All this, completely analogous to the EW and MH classes, confirms and strengthens earlier conclusions [23][24][25][26]30].…”

“…We also have b = −2β, since the width w 2 (t; ∞) = C(t, t; 0) = t −b F C (1, 0). This is justified since the initial conditions in the 1D KPZ do not generate new, independent renormalisations [30].…”

“…A systematic analysis of the invariance properties of the dynamical functionals studied for instance in [30,33,34], or the alternate form derived in [43], would be of interest, following the lines of study for the analysis of dynamical symmetries in phase-ordering kinetics, see [14] and refs. therein.…”

Dynamic simulations of the Kosterlitz-Thouless phase transition

“…[5] is calculated by taking our z as input. .0680 (11) .0695 (16) .0690 (17) .0682 (21) .0674 (12) .0650 (21) 0.0671 (21) .0691 (18) .0676 (12) .0685(08) .0682 (17) .0699 (22) .0668 (20) .0727 (28) .0768 (15) .0753 (22) .0774 (14) .0762 (26) .0784 (24) .0781 (11) .0768 (19) .0773 (13) .0777 (11) .0754 (16) .0778 (18) .0835(42) .0777 (12) .0705(46) .0781 (19) .0900 (24) . The upper and lower solid lines correspond to temperatures T 1 = 0.955 and T 2 = 0.965.…”

Logarithmic correlators or responses in non-relativistic analogues of conformal invariance

“…together with the generalised Family-Vicsek scaling [62,12,18,21,67,48]. The autoresponse exponent is read off from f χ (y) ∼ y −λ R /z for y → ∞.…”