We investigate the dynamical stability of a fully coupled system of N inertial rotators, the so-called Hamiltonian Mean Field model. In the limit N→∞, and after proper scaling of the interactions, the μ-space dynamics is governed by a Vlasov equation. We apply a nonlinear stability test to...

We discuss the equilibrium statistical mechanics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system from the canonical description of a stochastically forced Brownian system. We show that the mean-field approximation is exact in...

The nonlinear Klein–Gordon equation with a different potential that satisfies the degeneracy properties discussed in this paper possesses solitonic solutions that interact with long-range forces. We generalize the Ginzburg–Landau equation in such a way that the topological defects supported...

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...

We consider systems in which the canonical partition function can be expressed as the integral in an n-dimensional space (the order parameter space) of a function that also depends parametrically on the number N of degrees of freedom and on the inverse temperature β. We show how to compute,...

We discuss the possibility of using generalized canonical distributions, i.e., using other factors than exp(-βE), in order to compute the equilibrium properties of physical systems. It will be shown that some other choices can, in certain cases, lead to a simpler calculation of those...

We present a numerical study of the self-affine profiles obtained from configurations of the Ising model in d=1 with long-range interactions decaying with distance r as J(r)∼r−(1+ζ) for the cases ζ=0.3 and 0.5. The second-order static phase transition of this model is located by sharp...

In this work we study the effects of introducing long-range interactions in the Bak–Sneppen (BS) model of biological evolution. We analyze a recently proposed version of the BS model where the interactions decay as r−α; in this way, the first nearest neighbors model is recovered in the...

We investigate different mechanisms for the excitation of soliton internal degrees of freedom and for the existence of long-range interactions between solitons. We will study a nonlocal Klein–Gordon equation that is used as a model for Josephson junctions in thin films. We will show the...

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...