A simple solid-on-solid model of epitaxial thin films growth: surface roughness and dynamics

The random deposition model must be enriched to reflect the variety of surface roughness due to some material characteristics of the film growing by vacuum deposition or sputtering. The essence of the computer simulation in this case is to account for possible surface migration of atoms just after the deposition, in connection with binding energy between atoms (as the mechanism provoking the diffusion) and/or diffusion energy barrier. The interplay of these two factors leads to different morphologies of the growing surfaces from flat and smooth ones, to rough and spiky ones. In this paper we extended our earlier calculation by applying some extra diffusion barrier at the edges of terrace-like structures, known as Ehrlich-Schwoebel barrier. It is experimentally observed that atoms avoid descending when the terrace edge is approach and these barriers mimic this tendency. Results of our Monte Carlo computer simulations are discussed in terms of surface roughness, and compared with other model calculations and some experiments from literature. The power law of the surface roughness $\sigma$ against film thickness $t$ was confirmed. The nonzero minimum value of the growth exponent $\beta$ near 0.2 was obtained which is due to the limited range of the surface diffusion and the Ehrlich-Schwoebel barrier. Observations for different diffusion range are also discussed. The results are also confronted with some deterministic growth models.Comment: 12 pages + 8 figures (to appear in Int. J. Mod. Phys. C, journal style applied

Square lattice site percolation at increasing ranges of neighbor interactions

We report site percolation thresholds for square lattice with neighbor interactions at various increasing ranges. Using Monte Carlo techniques we found that nearest neighbors (N$^2$), next nearest neighbors (N$^3$), next next nearest neighbors (N$^4$) and fifth nearest neighbors (N$^6$) yield the same $p_c=0.592...$. At odds, fourth nearest neighbors (N$^5$) give $p_c=0.298...$. These results are given an explanation in terms of symmetry arguments. We then consider combinations of various ranges of interactions with (N$^2$+N$^3$), (N$^2$+N$^4$), (N$^2$+N$^3$+N$^4$) and (N$^2$+N$^5$). The calculated associated thresholds are respectively $p_c=0.407..., 0.337..., 0.288..., 0.234...$. The existing Galam--Mauger universal formula for percolation thresholds does not reproduce the data showing dimension and coordination number are not sufficient to build a universal law which extends to complex lattices.Comment: 4 pages, revtex

Comment on "Mean-field solution of structural balance dynamics in nonzero temperature"

In recent numerical and analytical studies, Rabbani {\it et al.} [Phys. Rev. E {\bf 99}, 062302 (2019)] observed the first-order phase transition in social triads dynamics on complete graph with $N=50$ nodes. With Metropolis algorithm they found critical temperature on such graph equal to 26.2. In this comment we extend their main observation in more compact and natural manner. In contrast to the commented paper we estimate critical temperature $T^c$ for complete graph not only with $N=50$ nodes but for any size of the system. We have derived formula for critical temperature $T^c=(N-2)/a^c$, where $N$ is the number of graph nodes and $a^c\approx 1.71649$ comes from combination of heat-bath and mean-field approximation. Our computer simulation based on heat-bath algorithm confirm our analytical results and recover critical temperature $T^c$ obtained earlier also for $N=50$ and for systems with other sizes. Additionally, we have identified---not observed in commented paper---phase of the system, where the mean value of links is zero but the system energy is minimal since the network contains only balanced triangles with all positive links or with two negative links. Such a phase corresponds to dividing the set of agents into two coexisting hostile groups and it exists only in low temperatures.Comment: 7 pages, 6 figures, 1 tabl

Reshuffling spins with short range interactions: When sociophysics produces physical results

Galam reshuffling introduced in opinion dynamics models is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature T_C \approx 3.09 [J/k_B] is recovered almost exactly, it is proved to be different from both values, not reshuffled (T_C=2/arcsinh(1) \approx 2.27 [J/k_B]) and mean-field (T_C=4 [J/k_B]). On this basis, gradual reshuffling is studied as function of 0 \leq p \leq 1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of T_C as function of p is obtained and exhibits a non-linear behavior. The simplest Solomon network realization is noted to reproduce Galam p=1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean-field values.Comment: 11 pages, 5 figures in 6 eps files, to appear in IJMP

Average distance in growing trees

Two kinds of evolving trees are considered here: the exponential trees, where subsequent nodes are linked to old nodes without any preference, and the Barab\'asi--Albert scale-free networks, where the probability of linking to a node is proportional to the number of its pre-existing links. In both cases, new nodes are linked to $m=1$ nodes. Average node-node distance $d$ is calculated numerically in evolving trees as dependent on the number of nodes $N$. The results for $N$ not less than a thousand are averaged over a thousand of growing trees. The results on the mean node-node distance $d$ for large $N$ can be approximated by $d=2\ln(N)+c_1$ for the exponential trees, and $d=\ln(N)+c_2$ for the scale-free trees, where the $c_i$ are constant. We derive also iterative equations for $d$ and its dispersion for the exponential trees. The simulation and the analytical approach give the same results.Comment: 6 pages, 3 figures, Int. J. Mod. Phys. C14 (2003) - in prin

Spreading gossip in social networks

We study a simple model of information propagation in social networks, where two quantities are introduced: the spread factor, which measures the average maximal fraction of neighbors of a given node that interchange information among each other, and the spreading time needed for the information to reach such fraction of nodes. When the information refers to a particular node at which both quantities are measured, the model can be taken as a model for gossip propagation. In this context, we apply the model to real empirical networks of social acquaintances and compare the underlying spreading dynamics with different types of scale-free and small-world networks. We find that the number of friendship connections strongly influences the probability of being gossiped. Finally, we discuss how the spread factor is able to be applied to other situations.Comment: 10 pages, 16 figures, Revtex; Virt.J. of Biol. Phys., Oct.1 200

New algorithm for the computation of the partition function for the Ising model on a square lattice

A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising antiferromagnet for a $8\times 8$ square lattice with open boundary conditions. The results agree qualitatively with the prediction of the Monte Carlo simulations and with experimental data and they are better than the mean field approach results. For the $8\times 8$ lattice, the algorithm reduces the computation time by nine orders of magnitude.Comment: 7 pages, 3 figures, to appear in Int. J. Mod. Phys.

Cooperation and defection in ghetto

We consider ghetto as a community of people ruled against their will by an external power. Members of the community feel that their laws are broken. However, attempts to leave ghetto makes their situation worse. We discuss the relation of the ghetto inhabitants to the ruling power in context of their needs, organized according to the Maslow hierarchy. Decisions how to satisfy successive needs are undertaken in cooperation with or defection the ruling power. This issue allows to construct the tree of decisions and to adopt the pruning technique from the game theory. Dynamics of decisions can be described within the formalism of fundamental equations. The result is that the strategy of defection is stabilized by the estimated payoff.Comment: 12 pages, 2 figure

Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination

The Ising model S=1/2 and the S=1 model are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well known 2d Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2d Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.Comment: 9 pages, 11 figure