Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPersistence in the zero-temperature dynamics of the $Q$-states Potts model on undirected-directed Barabasi-Albert networks and Erdos-Renyi random graphs
229
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384 $,..., $2^{30}$ states on {it directed} and {it undirected} Barabasi-Albert networks and Erdos-Renyi random graphs. In this model it is found that $P(t)$ decays exponentially to zero in short times for {it directed} and {it undirected} Erdos-Renyi random graphs. For {it directed} and {it undirected} Barabasi-Albert networks, in contrast it decays exponentially to a constant value for long times, i.e, $P(infty)$ is different from zero for all $Q$ values (here studied) from $Q=3,4,5,..., 2^{30}$; this shows blocking for all these $Q$ values. Except that for $Q=2^{30}$ in the {it undirected} case $P(t)$ tends exponentially to zero; this could be just a finite-size effect since in the other blocking cases you may have only a few unchanged spins.
rate research
Read More
Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order-disorder phase transition, the critical noise parameter $q_c$, as well as the critical exponents $beta/nu$, $gamma/nu$ and $1/nu$ have been calculated as a function of the connectivity $z$ of the random graph.
Using Monte Carlo simulations, we study the evolution of contigent cooperation and ethnocentrism in the one-move game. Interactions and reproduction among computational agents are simulated on {it undirected} and {it directed} Barabasi-Albert (BA) networks. We first replicate the Hammond-Axelrod model of in-group favoritism on a square lattice and then generalize this model on {it undirected} and {it directed} BA networks for both asexual and sexual reproduction cases. Our simulations demonstrate that irrespective of the mode of reproduction, ethnocentric strategy becomes common even though cooperation is individually costly and mechanisms such as reciprocity or conformity are absent. Moreover, our results indicate that the spread of favoritism toward similar others highly depends on the network topology and the associated heterogeneity of the studied population.
Monte Carlo simulations are performed to study the two-dimensional Potts models with q=3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and second-order phase transition is found for q=3 depending on the rewiring probability $p$, but for q=4 the system presents only a first-order phase transition for any value $p$ . This critical behavior is different from the Potts model on a square lattice, where the second-order phase transition is present for $qle4$ and a first-order phase transition is present for q>4.
We check the existence of a spontaneous magnetisation of Ising and Potts spins on semi-directed Barabasi-Albert networks by Monte Carlo simulations. We verified that the magnetisation for different temperatures $T$ decays after a characteristic time $tau(T)$, which we extrapolate to diverge at positive temperatures $T_c(N)$ by a Vogel-Fulcher law, with $T_c(N)$ increasing logarithmically with network size $N$.
Using Monte Carlo simulations we study the Ising model with spin S=1/2 and 1 on {it directed} and {it undirected} Erdos-Renyi (ER) random graphs, with $z$ neighbors for each spin. In the case with spin S=1/2, the {it undirected} and {it directed} ER graphs present a spontaneous magnetization in the universality class of mean field theory, where in both {it directed} and {it undirected} ER graphs the model presents a spontaneous magnetization at $p = z/N$ ($z=2, 3, ...,N$), but no spontaneous magnetization at $p = 1/N$ which is the percolation threshold. For both {it directed} and {it undirected} ER graphs with spin S=1 we find a first-order phase transition for z=4 and 9 neighbors.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
