Critical behavior of the random-field Ising model with long-range   interactions in one dimension
  We study the critical behavior of the one-dimensional random field Ising model (RFIM) with long-range interactions ($\propto r^{-(d+\sigma)}$) by the nonperturbative functional renormalization group. We find two distinct regimes of critical behavior as a function of $\sigma$, separated by a critical value $\sigma_c$. What distinguishes these two regimes is the presence or not of a cusp-like nonanalyticity in the functional dependence of the renormalized cumulants of the random field at the fixed point. This change of behavior can be associated to the characteristics of the large-scale avalanches present in the system at zero temperature. We propose ways to check these predictions through lattice simulations. We also discuss the difference with the RFIM on the Dyson hierarchical lattice. 
Ivan Balog, Gilles Tarjus and Matthieu Tissier
cond-mat.stat-mech