Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMonte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees
775
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We perform Monte-Carlo simulations to study the Bernoulli ($p$) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two different percolation thresholds $p_{c1}$ and $p_{c2}$. All the points in the intermediate phase $(p_{c1} < p < p_{c2})$ are critical and there exist infinitely many infinite clusters in the intermediate phase. In this phase the corresponding fractal exponent continuously increases with $p$ from zero to unity.
rate research
Read More
We investigate the scaling of the interfacial adsorption of the two-dimensional Blume-Capel model using Monte Carlo simulations. In particular, we study the finite-size scaling behavior of the interfacial adsorption of the pure model at both its first- and second-order transition regimes, as well as at the vicinity of the tricritical point. Our analysis benefits from the currently existing quite accurate estimates of the relevant (tri)critical-point locations. In all studied cases, the numerical results verify to a level of high accuracy the expected scenarios derived from analytic free-energy scaling arguments. We also investigate the size dependence of the interfacial adsorption under the presence of quenched bond randomness at the originally first-order transition regime (disorder-induced continuous transition) and the relevant self-averaging properties of the system. For this ex-first-order regime, where strong transient effects are shown to be present, our findings support the scenario of a non-divergent scaling, similar to that found in the original second-order transition regime of the pure model.
We have used the Monte Carlo (MC) simulation method with Metropolis algorithm to study the finite temperature phase transition properties of a binary alloy spherical nanoparticle with radius $r$ of the type $A_{p}B_{1-p}$. The system consists of two different species of magnetic components, namely, $A$ and $B$, and the components of the system have been selected $A$ and $B$ to be as $sigma = 1/2$ and $S=1$, respectively. A complete picture of phase diagrams, total magnetizations and susceptibilities in related planes have been presented, and the main roles of the radius of nanoparticle, active concentration value of type-$A$ atoms as well as other system parameters on the thermal and magnetic phase transition features of the considered system have been discussed in detail. Our MC investigations clearly show that it is possible to control the critical characteristic behaviors of the system with the help of adjustable Hamiltonian parameters.
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final static configuration of spanning clusters. A finite size scaling theory for such transition is developed and numerically verified. The scaling functions are found to depend on both g and rho. The singularities at the critical growth probability gc of a given rho are described by appropriate critical exponents. The values of the critical exponents are found to be same as that of the original percolation at all values of rho at the respective gc . The model then belongs to the same universality class of percolation for the whole range of rho.
Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering -- both in short-range (EA) and infinite-range (SK) models -- within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the $pm J$ EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of {it two} percolating clusters of {it unequal} densities.
We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov (LS) power-law growth in all the cases.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
