Critical exponents of the Ising model on low-dimensional fractal media

The critical behavior of the Ising model on fractal substrates with noninteger Hausdorff dimension d_H<2 and infinite ramification order is studied by means of the short-time critical dynamic scaling approach. Our determinations of the critical temperatures and critical exponents β, γ, and ν are compared to the predictions of the Wilson-Fisher expansion, the Wallace-Zia expansion, the transfer matrix method, and more recent Monte Carlo simulations using finite-size scaling analysis. We also determined the effective dimension (d_ef), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship d_ef=2β/ν+γ/ν. Furthermore, we obtained the dynamic exponent z of the nonequilibrium correlation length and the exponent θ that governs the initial increase of the magnetization. Our results are consistent with the convergence of the lower-critical dimension towards d=1 for fractal substrates and suggest that the Hausdorff dimension may be different from the effective dimension.     

Risk analysis in investment appraisal based on the Monte Carlo simulation technique by A. Hacura, M. Jadamus-Hacura and A. Kocot

Comment on Eur. Phys. J. B 20, 551 (2001) Since Hertz major work on investment appraisal using the Monte Carlo Simulation technique, the so called “Risk Analysis” has become a standard tool for supporting investment decisions [1,2]. A main problem in investment appraisal is to consider and specify the risk of investment projects in an appropriate way, for enabling consistent project evaluation. In calculating a risky project's net present value (NPV) the major difficulty is to quantify the project's risk for quantifying an appropriate risk adjusted discount rate (RADR). Theoretically not founded risk adjusted discount rates face a lot of critique. Furthermore it is discussed that the incorporation of a constant risk factor into the discount rate makes a certain assumption about the resolution of uncertainty over time [3] and finally that a single net present value could not in general reflect risk properly. Especially in consequence of the last point the proponents of simulation argue that a whole distribution of net present values shows a project's risk better than a single number. In the special issue “Econophysics” of this journal Hacura et al. tried to describe the methodology and use of Monte Carlo Simulation in investment appraisal [4]. The purpose of this comment is to point out three fundamental flaws in that article. Received 29 April 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: robert.obermaier@wiwi.uni-regensburg.de     

Monte Carlo Simulation of Optical Properties of Wake Bubbles

Based on Mie scattering theory and the theory of multiple light scattering, the light scattering properties of air bubbles in a wake are analysed by Monte Carlo simulation. The results show that backscattering is enhanced obviously due to the existence of bubbles, especially with the increase of bubble density, and that it is feasible to use the Monte Carlo method to study the properties of light scattering by air bubbles.     

Monte Carlo simulation of the reorientation transition in Heisenberg model with dipole interactions

The change of magnetic states in ultrathin films with temperature have been simulated by Monte Carlo method. A Heisenberg model with long-range dipole interactions was adopted in our calculations. The results were qualitatively in good agreement with the experimental phenomena. That is at low temperatures the magnetization is perpendicular to the plane, and at higher temperatures but below the Curie point, the magnetization is mostly within the plane. In between these two regions, the magnetization seems to be suppressed. The simulations show that the loss of magnetization is a consequence of the special magnetic states in which the local domains orientations are reverse with the neighbor ones.     

Monte Carlo simulation of three-dimensional dilute Ising model

A multispin coding program for site-diluted Ising models on large simple cubic lattices is described in detail. The spontaneous magnetization is computed as a function of temperature, and the critical temperature as a function of concentration is found to agree well with the data of Marro et al.⁽⁴⁾ and Landau⁽³⁾ for smaller systems.The first successful epsilon expansion seems to be by D. E. Khmelnitskii,ZhETF 68:1960 (1975), English translationSov. Phys. JETP 41:981 (1975); for numerical estimates see K. E. Newman and E. K. Riedel,Phys. Rev. H25:264 (1982), for experiments see R. J. Birgenau, R. A. Cowley, G. Shirane and H. Yoshizawa,J. Stat. Phys. 34:817 (1984).     

Monte Carlo simulation of spin-wave excitation for the magnetic films with structure and interaction fluctuations

Monte Carlo simulation studies are performed to examine influence of structure and interaction fluctuations on magnetic properties of a ferromagnetic system modelled with a Heisenberg Hamiltonian. It is found that the spontaneous magnetization at low temperature for the multilayered films decreases with temperature in a Bloch law of spin-wave excitations. Both Bloch coefficient B and exponent b vary evidently because of a strong surface and size effect in the finite magnetic films with free boundaries. For the disordered bulk FCC magnet with periodic boundary, the Bloch T^3/2 law is followed at low temperature and B is greatly influenced by the structure and interaction fluctuations. At the same time, Bloch coefficient B of the amorphous magnet with the coordination and interaction fluctuations has been derived. The simulated results are in good agreement with the theoretical predictions of spin-wave excitation, and explain the experimental facts well.     

Transient Non-Thermal Mobility of CO for CO--NO Catalytic Reaction on Square Lattice: Monte Carlo Simulation

We study a model based on precursor mechanism for CO-NO catalytic reaction on square lattice with Monte Carlo simulation. The precursor mechanism clearly demonstrates its impact on the phase diagram. The steady reactive state （SRS） gets established. The width of reactive region increases by increasing the range of precursor mobility. When the precursor mobility is increased to third-nearest neighbourhood, the second-order transition disappears.     

Critical behavior of the 3D Ising model on a poissonian random lattice

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D ferromagnetic Ising model on 3D Voronoi-Delauney lattices. It is assumed that the coupling factor J varies with the distance r between the first neighbors as J(r)∝e^−ar, with a≥0. The critical exponents γ/ν, β/ν, and ν are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure 3D ferromagnetic Ising model.     

Risk analysis in investment appraisal based on the Monte Carlo simulation technique

This work has been prepared for the purpose of presenting the methodology and uses of the Monte Carlo simulation technique as applied in the evaluation of investment projects to analyze and assess risk. In the deterministic appraisal the basic decision rule for a project is simply to accept or reject the project depending on whether its net present value (NPV) is positive or negative, respectively. Similarly, when choosing among alternative (mutually exclusive) projects, the decision rule is to select the one with the highest NPV, provided that it is positive. Recognizing the fact that the key project variables (as: volume of sales, sales price, costs) are not certain, an appraisal report is usually supplemented to include sensitivity and scenario analysis tests. Both tests are static and rather arbitrary in their nature. During the simulation process, random scenarios are built up using input values for the project's key uncertain variables, which are selected from appropriate probability distributions. The results are collected and analyzed statistically so as to arrive at a probability distribution of the potential outcomes of the project and to estimate various measures of project risk. Received 25 September 2000     

Monte Carlo simulation of cluster kinetics in three-dimensional Ising model

Simulations in lattices of size 100³ at the critical point of the three-dimensional Glauber kinetic Ising model indicate that the 1935 Becker-Doring equation no longer works there: The growth rates decay in time. These conclusions confirm those in two dimensions.     

Critical properties of the three-dimensional Ising model with quenched disorder

The static critical properties of the three-dimensional Ising model with quenched disorder are studied by the Monte-Carlo (MC) method on a simple cubic lattice, in which the quenched disorder is distributed as nonmagnetic impurities by the canonical manner. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.0; 0.95; 0.9; 0.8; 0.7; 0.6. The systems of non-linear sizes L×L×L, L=20-60 are researched. On the basis of the finite-size scaling (FSS) theory, the static critical exponents of specific heat α, susceptibility γ, magnetization β, and an exponent of the correlation radius in a studied interval of concentrations p are calculated. It is shown that the three-dimensional Ising model with quenched disorder has two regimes of the critical behavior universality in a dependence on nonmagnetic impurities.     

Local structure of Co and Ni in decagonal AlNiCo investigated by polarized EXAFS

The local structure of cobalt and nickel in single crystals of decagonal quasicrystals with composition Al_71.5Ni_15.5Co₁₃ and Al₇₅Ni_14.5Co_10.5 have been studied by polarized EXAFS. Significant differences between the Ni and Co local environments have been detected. The effective absence of the 4 ? periodicity along the decagonal axis in these QCs is confirmed and indications about its reasons are presented. Received 26 July 2000 and Received in final form 20 October 2000     

Monte Carlo simulation of two-dimensional Ising model with logarithmic exchange interaction

Monte Carlo simulation was done to a 2-D Ising model with exchange interaction depending logarithmically on distance. This model is equivalent to a 2-D Coulomb gas.A configuration corresponding to bound pairs of opposite charges appears below T_c, while above T_c pairs are dissolved into free charges.     

Monte Carlo simulation of a random-field Ising antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.     

Monte Carlo simulation of a kinetic Ising model of the glass transition

Results of Monte Carlo experiments for the two-spin facilitated kinetic Ising model on a cubic lattice are presented and compared with a theoretical prediction.     

The exchange bias and coercivity of FM/AFM films: Monte Carlo simulation

The exchange bias (H_E) and coercivity (H_C) of the ferromagnet/antiferromagnet (FM/AFM) films have been simulated with Monte Carlo method. The simulated results indicate that, the value of H_E decreases with increasing temperature, and the values of H_E and the blocking temperature T_b at which H_E=0 reduce evidently with decreasing absolute value of interlayer exchange coupling JI. It also is found that for the large absolute values of JI, the maximum in H_C occurs very close to T_b. At the same time, it is observed that the diluted ratio of FM at FM/AFM interface influences clearly the value of H_E. The simulated results are consistent with the experimental facts. The maximum behaviour in the H_C−T curves has been explained by the interplay of the softening of some fraction of the spins in the AFM layer near T_N′ and the disorder of the spins in FM layer near Curie temperature T_C.     

Inelastic neutron scattering study of the dynamics of the AlNiCo decagonal phase

The dynamics of the decagonal AlNiCo phase has been investigated on a single-grain quasicrystalline sample using inelastic neutron scattering. The decagonal structure can be viewed as a periodic stacking of quasiperiodic planes. The anisotropy between the modes propagating in the periodic and quasiperiodic directions is found to be much weaker than theoretically predicted. A strong resonance splitting is observed at an energy transfer of 15 meV for transverse modes polarized in the quasiperiodic plane. Received: 18 November 1998 / Accepted: 27 November 1998     

Secondary structure prediction of beta-hairpin peptide tryptophan zipper-I

We have investigated the folding properties of tryptophan zipper-I molecule which folds into a stable β-hairpin motif in aqueous solution as suggested by nuclear magnetic resonance (NMR) experiments. An all-atom presentation, including hydrogen, was used with an implicit solvent. As a simulation technique, simulated tempering algorithm was used to obtain equilibrium conformations of the molecule at ten distinct temperatures. Our minimum energy configuration obtained from simulated tempering algorithm is a β-hairpin motif with 1.30 Å backbone root-mean-square deviation from the reference PDB structure (1le0.pdb). Several quantities and exhaustive folding free energy landscapes were determined and discussed in order to clarify the folding behavior.     

Monte Carlo simulation of very large kinetic Ising models

We study the relaxation of Ising models in three and four dimensions aboveT _c , using multi-spin coding for lattices up to 360³ and 40⁴. The nonlinear relaxation time diverges as (T–T _c )^{–1.05±0.04} in three dimensions, where corrections to scaling are taken into account. In four dimensions the effective exponent is about 0.72; logarithmic correction factors make the analysis difficult here. The linear relaxation time for the asymptotic exponential decay is found to be larger, with effective exponents 1.31 (d=2) and 0.97 (d=4). The difference in the linear and nonlinear relaxation exponents is compatible in three dimensions with the orderparameter exponent , as predicted by Racz.Work supported by SFB 125 Aachen-Jülich-KölnWork started at Department de Physique des Systemes Desordonnes, Universite de Provence, Centre St-Jerome, F-13397 Marseille Cedex 13, France