In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to...

One- and two-dimensional lattices of points are connected with long-range links, whose lengths are distributed according to P(r)∼r-μ. By changing the decay exponent μ one can go from d-dimensional short-range networks to ∞-dimensional networks topologically similar to random graphs. An...

The zeros of the partition function of the ferromagnetic q-state Potts model with long-range interactions in the complex-q plane are studied in the mean-field case, while preliminary numerical results are reported for the finite 1d chains with power-law decaying interactions. In both cases, at...

We present the numerical study of the one-dimensional Potts model with power-law decaying ferromagnetic interactions. The largest cluster probability distribution is obtained by Monte Carlo simulations using the Swendsen–Wang cluster algorithm with cumulative probabilities. The finite-size...

Two-dimensional lattices of points are connected with long-range links, whose lengths are distributed according to P(r)∼r-α. By changing the decay exponent α one can go from d-dimensional short-range networks to ∞-dimensional networks topologically similar to random graphs. Percolation on...

The nonextensivity of a classical long-range Hamiltonian system is discussed. The system is the so-called α-XY model, a lattice of inertial rotators with an adjustable parameter α controlling the range of the interactions. This model has been explored in detail over the last years. For...

A stochastic one-dimensional cellular automaton with long range spatial interactions is introduced. In this model the state probability of a given site at time t depends on the state of all the other sites at time t−1 through a power law of the type 1/rα, r being the distance between sites....