Scientific Calendar Event

Starts 28 May 2024 11:00
Ends 28 May 2024 12:00
Central European Time
room 138 (SISSA, via Bonomea) and via Zoom

Federico Corberi
(Università di Salerno)

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.  

[1] F. Corberi, and C. Castellano, arXiv:2309.16517 (to appear in J.Phys: Complexity, 2024).
[2] F. Corberi, and L. Smaldone, Phys. Rev. E 109, 034133 (2024).
[3] F. Corberi, and L. Smaldone, arXiv:2402.11079 (to appear in J. Stat. Mech., 2024).
[4] F. Corberi, E. Lippiello, and P. Politi, J. Stat. Phys. 176, 510 (2019).
[5] A.J. Bray, and A.D. Rutenberg, Phys. Rev. E 49, R27 (1994).
[6] A.D. Rutenberg, and A.J. Bray, Phys. Rev. E 50, 1900 (1994).