Monte Carlo Renormalization Group Analysis Research Articles

Monte Carlo renormalization-group analysis of percolation

We describe a Monte Carlo renormalization group approach to the calculation of critical behavior for percolation models. This approach can be utilized to determine the renormalized bond probabilities and the values of the critical exponents. We illustrate the method for two-dimensional bond percolation, but the method is also applicable to other percolation models and other dimensions.

Critical behavior of the ferromagnetic Ising model on a Sierpiński carpet: Monte Carlo renormalization group study

We perform a Monte Carlo renormalization group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski fractal with Hausdorff dimension ${d}_{f}\ensuremath{\simeq}1.8928.$ This method is shown to be relevant to the calculation of the critical temperature ${T}_{c}$ and the magnetic eigenexponent ${y}_{h}$ on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigenexponent ${y}_{t}.$ At last, the results are shown to be consistent with a finite-size scaling analysis.

Monte Carlo renormalization group analysis of QCD in two dimensional coupling space

We report our result of the Monte Carlo Renormalization Group analysis in two dimensional coupling space. The qualitative feature of the RG flow is described with a phenomenological RG equation. The data on the lattice spacing for various actions serve the condition to determine the parameters.

Monte Carlo Renormalization Group analysis of QCD in two dimensional coupling space

Monte Carlo Renormalization Group analysis of QCD in two dimensional coupling space

Scaling study of pure gauge lattice QCD by Monte Carlo renormalization group method.

The scaling behavior of pure gauge SU(3) in the region $\beta=5.85 - 7.60$ is examined by a Monte Carlo Renormalization Group analysis. The coupling shifts induced by factor 2 blocking are measured both on 32$^4$ and 16$^4$ lattices with high statistics. A systematic deviation from naive 2-loop scaling is clearly seen. The mean field and effective coupling constant schemes explain part, but not all of the deviation. It can be accounted for by a suitable change of coupling constant, including a correction term ${\cal O}(g^7)$ in the 2-loop lattice $\beta$-function. Based on this improvement, $\sqrt{\sigma}/\Lambda_{\overline {MS}}^{n_f=0}$ is estimated to be $2.2(\pm 0.1)$ from the analysis of the string tension $\sigma$.

Monte Carlo renormalization group study at large β in confinement region

Monte Carlo renormalization group analysis on SU(3) lattice at large β is studied. On 32 4 lattice, coupling shift Δβ is 0.48 ± 0.02 and 0.53 ± 0.02 at β=6.55 and 6.80, where the lattice remains in confinement phase. Δβ is approaching its 2-loop asymptotic scaling value. However, deviation is still 20% and 13% at β=6.55 and 6.80, respectively. We also report high statistics data on 16 4 lattice at β=6.80, giving Δβ = .52 ± 0.03 in the deconfined regime.

Scaling structure in simple screening models for columnar growth.

Several versions of a simplified oblique incidence ballistic deposition model introduced by Nagatani [J. Phys. A 24, L449 (1991)] have been explored using computer simulations and theoretical approaches. In these models self-similar columnar patterns characterized by an algebraic distribution of heights evolve as a consequence of the competition among columns for the incoming flux. The growth rate of each column is a nonlinear function of its height. The competition is driven by the shot noise in the deposition process or, for a deterministic version of the model, by the amplification of disorder in the initial state of the surface. We find excellent agreement between simulation results and the theoretical analysis. However, our results appear to differ substantially from those obtained by Nagatani using smaller-scale simulations and a Monte Carlo renormalization-group analysis. In particular, we indicate how a spurious dependence of the height distribution exponent on the angle of incidence may arise from crossover effects. In the deterministic case the height distribution exponent depends continuously on the distribution of initial disorder.

Fixed points and domain growth for the Potts model.

We present a Monte Carlo renormalization-group analysis of the dynamics of the eight-state Potts model with nearest- and next-nearest-neighbor interactions after a quench below its phase-transition point. Our results sugest the existence of at least two distinct fixed points at zero temperature. One is associated with a freezing behavior while the second is associated with equilibration. Our conclusion is that the freezing fixed point is only attractive for quenches to zero temperature, while the equilibration fixed point is attractive for quenches to finite temperature.

An improved renormalization group transformation in four dimensions

A new transformation for Monte Carlo renormalization group analysis of four-dimensional gauge theories is developed. This RG transformation has a scale factor of √3. In addition no gauge fixing is required in the construction of the link variables on the renormalized lattice. The Z(2) theory is analyzed as a test case.

Floating phase in the chiral Potts model. A Monte Carlo renormalization-group analysis

Layers of atoms or molecules adsorbed on surfaces may exhibit floating critical phases. To investigate this phenomenon we have developed a Monte Carlo renormalization-group scheme and performed calculations on the three-state chiral Potts model. The results indicate a continuous transition from a floating phase to a liquid phase at a temperature much higher than that found by series-expansion methods.

Properties of theq-state clock model forq=4, 5, and 6

The two-dimensional clock models for $q=4, 5, \mathrm{and} 6$ were simulated on lattices of size 256 and 1024. Various properties were computed including the specific heat, susceptibility, vorticity, and correlation times. However, only a Monte Carlo renormalization-group analysis was capable of locating quantitatively the phase transitions for $q=5 \mathrm{and} 6$. The results agree with the qualitative picture obtained for the Villain version of the clock model. The relevance of this work to the two-dimensional melting problem is discussed. MS code no. BT2080 1977

Monte Carlo renormalization-group analysis of the antiferromagnetic three-state Potts model on a square lattice

Monte Carlo renormalization-group calculations have been performed on the three-state anti-ferromagnetic Potts model on a square lattice. The results are consistent with the conclusion that there is no transition as a function of temperature.

Monte Carlo renormalization-group analysis of the classical Heisenberg model in two dimensions

Monte Carlo renormalization-group methods were applied to the classical three-component Heisenberg model on a two-dimensional lattice. Expectation values of local correlations of spins and various sized block spins were computed using traditional Monte Carlo methods. By matching quantities at different length scales generated by different Monte Carlo Hamiltonians we directly determined the renormalization of the nearest-neighbor coupling. Using these data and the results of high-temperature expansions and low-temperature renormalization-group calculations we have determined that this model does not have a phase transition. We have also obtained the amplitude for the low-temperature divergence of the susceptibility and the correlation length.