Crossover and self-averaging in the two-dimensional site-diluted Ising model: Application of probability-changing cluster algorithm (original) (raw)
Related papers
Local and cluster critical dynamics of the 3d random-site Ising model
Physica A: Statistical Mechanics and its Applications, 2006
We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L = 10 − 96 are analysed by a finite-size-scaling technique. The site dilution concentration p = 0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.
Condensed Matter Physics, 2005
We apply numerical simulations to study of the criticality of the 3D Ising model with random site quenched dilution. The emphasis is given to the issues not being discussed in detail before. In particular, we attempt a comparison of different Monte Carlo techniques, discussing regions of their applicability and advantages/disadvantages depending on the aim of a particular simulation set. Moreover, besides evaluation of the critical indices we estimate the universal ratio Γ + /Γ − for the magnetic susceptibility critical amplitudes. Our estimate Γ + /Γ − = 1.67±0.15 is in a good agreement with the recent MC analysis of the random-bond Ising model giving further support that both random-site and random-bond dilutions lead to the same universality class.
Critical and thermodynamic properties of the randomly dilute Ising model
Physical Review B, 1978
The randomly bond-dilute two-dimensional nearest-neighbor Ising model on the square lattice is studied by renormalization-group methods based on the Migdal-Kadanoff approximate recursion relations. Calculations give both thermal and magnetic exponents associated with the percolative fixed point. DifFerential recursion relations yield a phase diagram which is in quantitative agreement with all known results. Curves for the specific heat, percolation probability, and magnetization are displayed. The critical region of the specific heat becomes unobservably narrow well above the percolation threshold p, , This provides a possible explanation for the apparent specific-heat rounding in certain experiments.
Physical Review E, 1999
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to put the equilibrium ensemble approach to work. A new method to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open in both directions. A critical discussion shows that, still, an unambiguous discrimination between the two scenarios is not possible on the basis of the available finite size data.
Journal of Statistical Physics, 1990
Finite square L • L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energy U, specific heat C, magnetization (]MI), susceptibility ~) and percolation cluster properties relating to the "physical clusters," namely the Fortuin-Kasteleyn clusters (percolation probability (P~), percolation susceptibility ~p, cluster size distribution n/) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, (P~) being identical to ([MI) in the thermodynamic limit, while finite-size corrections differ. In contrast, Xp differs from X even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes to )~, but not to )~p. Near Tc the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.
The four-dimensional site-diluted Ising model: A finite-size scaling study
Nuclear Physics B, 1998
Using finite-size scaling techniques, we study the critical properties of the site-diluted Ising model in four dimensions. We carry out a high statistics Monte Carlo simulation for several values of the dilution. The results support the perturbative scenario: there is only the Ising fixed point with large logarithmic scaling corrections. We obtain, using the Perturbative Renormalization Group, functional forms for the scaling of several observables that are in agreement with the numerical data.
Monte Carlo study of the square-lattice annealed Ising model on percolating clusters
Physical Review B, 1997
Simulations of an Ising q-state Potts model which is equivalent to the Ising model on annealed percolation clusters are used to determine the phase diagram of the model in two dimensions. Three topologically different phase diagrams are obtained: ͑i͒ for qϭ2, there are two critical Ising lines meeting at Tϭ0 at the four-state Potts critical point; ͑ii͒ for 2Ͻqр4, the Ising critical line meets the q-state critical line and a line of first-order transitions at a bicritical point; ͑iii͒ for qϾ4, the Ising critical line intersects a line of first-order transitions at a critical end point. ͓S0163-1829͑97͒06725-8͔
Phase diagram of the Ising model on percolation clusters
Physical Review B, 1994
The annealed Ising magnet on percolation clusters is studied by means of a mapping into a Potts-Ising model and with the Migdal-Kadanoff renormalization-group method. The phase diagram is determined in the three-dimensional parameter space of the Ising coupling E, the bond-occupation probability p, and the fugacity q, which controls the number of clusters. Three phases are identified: percolating ferromagnetic, percolating paramagnetic, and nonpercolating paramagnetic. For large q the phase diagram includes a multicritical point at the intersection of the Ising critical line and the percolation critical line.
Site-diluted Ising model in four dimensions
Physical Review E, 2009
In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.