Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform an exact enumeration. The main principles of Monte Carlo...

Monte Carlo algorithms are nearly always based on the concept of detailed balance and ergodicity. In this paper we focus on algorithms that do not satisfy detailed balance. We introduce a general method for designing non-detailed balance algorithms, starting from a conventional algorithm...

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a large number of degrees of freedom, and both short- and...

Several experimental techniques have shown that the primary response of many materials comes from a heterogeneous distribution of independently relaxing nanoscale regions; but most Monte Carlo simulations have homogeneous correlations. Resolving this discrepancy may require including the energy...

In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step–edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting crossover phenomena are identified. Simulational results...

We study an intrinsic curvature model defined on fixed-connectivity triangulated lattices enclosing a spherical core by using the canonical Monte Carlo simulation technique. We find that the model undergoes a discontinuous transition of shape transformation between the smooth state and a...

Using Monte Carlo techniques, the two-dimensional site-diluted Ising model is studied. In particular, properties of the specific heat, its critical behaviour and the emergence of a non-singular maximum above the transition temperature at moderate concentration of defects, are discussed.

In this paper, the percolation of mixtures of monomers and polyatomic species (k-mers) on a square lattice is studied. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing of the fraction of percolating lattices are found. A phase diagram separating a...

A model of surface deconstruction in 1+1 dimensions is presented in this paper. The process of decay goes on only at surface sites in a reaction-limited regime and the statistical properties of surface sites are studied in comparison with the well-known results of the Eden growth. In particular,...

The consequences of discretization on the resulting viscosity for the necklace model are analyzed to find out the mechanisms by which this model leads to results different from what could be anticipated. In order to accomplish this, various models of increasing complexity are proposed. First,...