Universality in the time correlations of the long-range 1d Ising model

The equilibrium and nonequilibrium properties of ferromagnetic systems may be affected by the long-range nature of the coupling interaction. Here we study the phase separation process of a one-dimensional Ising model in the presence of a power-law decaying coupling, with , and we focus on the two-time autocorrelation function . We find that it obeys the scaling form , where is the typical domain size at time t , and where can only be of two types. For , when domain walls diffuse freely, falls in the nearest-neighbour (nn) universality class. Conversely, for , when domain walls dynamics is driven, displays a new universal behavior. In particular, the so-called Fisher-Huse exponent, which characterizes the asymptotic behavior of for , is in the nn universality class ( ) and for .