Eur. Phys. J. B 63, 85-91 (2008)
https://doi.org/10.1140/epjb/e2008-00202-2

Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

¹ Laboratoire de Physique des Matériaux (Laboratoire associé au CNRS UMR 7556.) , Université Henri Poincaré Nancy I, B.P. 239, F-54506 Vandœuvre-les-Nancy Cedex, France
² Centro de Física Téorica e Computacional, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto 2, P-1649-003 Lisboa Codex, Portugal

Corresponding author: ^a henkel@lpm.u-nancy.fr

Received: 25 September 2007
Revised: 13 March 2008
Published online: 28 May 2008

Abstract

The non-equilibrium dynamics of the kinetic spherical model with a non-conserved order-parameter, quenched to T≤T_c from a fully disordered initial state, is studied at its upper critical dimension d=d^*=4. In the scaling limit where both the waiting time s and the observation time t are large and the ratio y=t/s>1 is fixed, the scaling functions of the two-time autocorrelation and autoresponse functions do not contain any logarithmic correction factors and the typical size of correlated domains scales for large times as L(t)∼t^1/2.