Colloquium

Growth kinetics and aging phenomena in a frustrated system^★

¹ Centre for Fluid and Complex Systems, Coventry University, CV1 5FB, Coventry, UK
² Dipartimento di Fisica “E. R. Caianiello”, and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno,Università di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
³ Department of Mathematics and Physics, University of Campania L. Vanvitelli, Viale Lincoln 5, 81100 Caserta, Italy
⁴ School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India

^a e-mail: purijnu@gmail.com

Received: 13 December 2019
Received in final form: 4 March 2020
Published online: 14 May 2020

Abstract

We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links a can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in a radical way. Small a does not prevent the system from a complete ordering, but this occurs in an extremely (logarithmically) slow manner. However, larger values of this parameter destroy complete ordering, due to frustration, and the evolution is comparatively faster (algebraic). Our study shows a precise correspondence between the kind of developing order, ferromagnetic versus frustrated, and the speed of evolution. The aging properties of the system are studied by focusing on the scaling properties of two-time quantities, the autocorrelation and linear response functions. We find that the contribution of an equilibrium and an aging part to these functions occurs differently in the various regions of the phase diagram of the model. When quenching inside the ferromagnetic phase, the two-time quantities are obtained by the addition of these parts. Instead, in the paramagnetic phase, these two contributions enter multiplicatively. Both of the scaling forms are shown with excellent accuracy, and the corresponding scaling functions and exponents have been determined and discussed.