Federico Corberi
(Università di Salerno)
 

Abstract:
I will present a thorough discussion of the ordering kinetics of ferromagnetic systems with long-range interactions decaying with distance as r^(-α), for any and in any spatial dimension d. I will consider two paradigmatic models: the voter model and the Ising one. The former is solvable in any dimension ^[1-3]. The latter can be studied analytically in one dimension using scaling arguments ^[4], or in a continuum (Ginzburg-Landau) approach ^[5,6]. Besides that, numerical simulations are also available. In general, the kinetics is characterized by the formation and growth of domains. In both models there is an upper critical value α_SR of α, such that for α>α_SR the model behaves as the corresponding one with short-range interactions (e.g. among nearest-neighbors). In particular, the characteristic size L(t) of the coarsening domains grows as L(t)∝t^(1/2). There also exists a lower critical value α_LR such that some mean-field features (corresponding to α=0), specifically the absence of a real coarsening regime, are displayed for α<α_LR. For intermediate values of alpha, for α_LR<α<α_SR, there is an algebraic growth of the domains L(t)∝t^(1/z) , with a non-trivial α-dependent value of the exponent z. A rich pattern of dynamical scaling violations are also observed as α and spatial dimension are varied. Besides that, the voter model is interested by the presence of non-equilibrium highly correlated stationary states whose lifetime diverges in the thermodynamic limit.