We present a generalized stochastic Cantor set by means of a simple cut and delete process and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, m and b, are introduced which tune the relative strength of the...

Temporal scaling and infinite variance are two stylized features often seen together in times series of complex systems. We find that because of their infinite moments samples from fractional Lévy flights produce bi-linear scaling functions which may be incorrectly attributed as evidence of...

In this paper we recursively describe the Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs. In particular, we study the Abelian Sandpile Model on these graphs and obtain the generating function of the recurrent configurations. Further, we give some exact...

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses dynamic...

By using the differential operator technique and the effective field theory scheme we study the tricritical behavior of Heisenberg classical model of spin-12 in a random field. The phase diagram in the T–h plane on a square and simple cubic lattice for a cluster with two spins is obtained when...

The effect of a random surface field, within the bimodal distribution, on the layering transitions in a spin-12 Ising thin film is investigated using Monte Carlo simulations. It is found that the layering transitions depend strongly on the concentration p of the disorder of the surface magnetic...

The phase diagram, the thermodynamic and ground-state critical properties of the random-field Ising model defined on the diamond family of hierarchical lattices with arbitrary dimension and scaling factor b=2 is investigated. The continuous Gaussian and the discrete delta-bimodal initial...

A recently derived Fokker–Planck equation for constrained systems is used to study the response of the pure and random field spherical models to sudden changes in external parameters (temperatures and strength of the random field).

The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The Sherrington–Kirkpatrick Ising spin glass with random...

The phase diagram of the Heisenberg ferromagnetic model in the presence of a magnetic random field (we have used bimodal distribution) of spin S=1/2 (quantum case) and S=∞ (classical case) on a simple cubic lattice is studied within the framework of the effective-field theory in finite cluster...