Monte Carlo study of the Yukawa coupled two-spin Ising model

We consider a particular four state spin system composed of two Ising spins (s_x, σ_x) with independent hopping parameters κ₁ κ₂, coupled by a bilinear Yukawa term, ys_xσ_x. The Yukawa term is solely responsible for breaking the global Z₂ × Z₂ symmetry down to Z2. This model is intended as an illustration of general coupled Higgs system where scalars can arise both as composite and elementary excitations. For the Ising example in 2d, we give convincing numerical evidence of the universality of the two-spin system with the one-spin Ising model, by Monte Carlo simulations and finite size scaling analysis. We also show that as we approach the phase transition, universality arises by having a single correlation length that diverges.     

Critical behavior of single crystal CuCr2Se4−x Br x (x=0.25)

The doping of bromine has prominent effect on the transport properties of CuCr₂Se₄, where the conductivity of CuCr₂Se_4?x Br _x changes from metallic behavior with x=0 to semiconductor with x=1. In this work, the critical behavior of single crystal CuCr₂Se_4?x Br _x with x=0.25, which lies at the boundary between the metallic and insulating state, is investigated through the magnetization under high magnetic field. The critical exponents β=0.39±0.03 and γ=1.25±0.05 are obtained by the Kouvel–Fisher method, and δ=4.79±0.01 is generated by the critical iso-thermal analysis. The obtained exponent β is close to the prediction of the three-dimensional (3D) Heisenberg model, while γ approaches that of the 3D-Ising model. Although the bromine doping has prominent effect on the transport behavior, the critical exponents are hardly changed. The obtained results indicate that the ferromagnetism is established through one-dimensional Cr–Se–Cr bonds. However, the nearest-neighbor magnetic interaction belonging to the 3D-Heisenberg model also contributes to the ferromagnetic exchange.     

Magnetic phase diagram of diluted spinel Zn1−xCuxCr2Se4 system

By using mean field theory, we have evaluated the nearest-neighbour and the next-neighbour super-exchange J₁(x) and J₂(x), respectively, for Zn_1−xCu_xCr₂Se₄ in the range 0?x?1. The intraplanar and the interplanar interactions are deduced. High-temperature series expansions are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation. The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The values are comparable to those of the 3D Heisenberg model, and are insensitive to the dilution x.     

Magnetic properties of magnetic Co1−xMgxFe2O4 spinel by HTSE method

Magnetic properties and exchange-coupling interactions of diluted magnetic spinels A_1−xA′_xB₂X₄, where A and B are magnetic ions, namely Co_1−xMg_xFe₂O₄, were investigated using the high-temperature series expansion method (HTSE) and the distribution method of magnetic cations in the range 0≤x≤1. The magnetic phase diagram and transition temperature versus dilution x were determined using the Padé approximants method along with HTSE. The critical exponent associated with the magnetic susceptibility γ was then deduced. The obtained results are in good agreement with experimental results and critical exponent values are consistent with those suggested by the universality hypothesis.     

A comparative study of the dynamic critical behavior of the four-state Potts like models

We investigate the short-time critical dynamics of the Baxter-Wu (BW) and n=3 Turban (3TU) models to estimate their global persistence exponent θ_g. We conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very difficult to obtain in usual simulations. In addition, we estimate again the dynamical exponents of the four-state Potts (FSP) model in order to compare them with results previously obtained for the BW and 3TU models and to decide between two sets of estimates presented in the current literature. We also revisit the short-time dynamics of the 3TU model in order to check if, as already found for the FSP model, the anomalous dimension of the initial magnetization x₀ could be equal to zero.     

Amorphous rare-earth alloys: random-anisotropy antiferromagnetism

The model of randomly oriented single-ion uniaxial anisotropy field is extended to the case of antiferromagnetic exchange interaction between rare-earth ions. A self-consistent two-spin cluster approximation is used to calculate the magnetization curves for a model system of spin 1. The results are in good qualitative agreement with experimental data on amorphous RE_xCu_1?x and RE_xAg_1?x alloys (RE = Tb, Dy, Ho). In particular, the observed increase of the “coercive” field with increasing x in RE_xCu_1?x alloys is accounted for.     

The effects of surfaces on dynamic critical behavior

The field theoretic renormalization-group approach for the study of critical behavior near free surfaces is generalized to dynamic properties. Time-dependent Ginzburg-Landau models with nonconserved or conserved order parameters — semi-infinite generalizations of the so-called modelsA andB — are considered. The asymptotic behavior of response and correlation functions is analyzed at the ordinary and special transitions in 4-? dimensions, and dynamic scaling laws for surface quantities are obtained. It is shown that the critical exponents can be expressed entirely in terms of static bulk and surface exponents andz, the dynamic bulk exponent. The critical exponents for the leading frequency, temperature and momentum singularities of the surface two-spin correlation function at the ordinary transition differ appreciably from the corresponding bulk analogues. In addition, the shape function which describes its frequency dependence differs qualitatively from the one of the bulk correlation function.     

Critical behavior in Ga-doped manganites La0.75(Sr,Ca)0.25Mn1−xGaxO3 (0≤x≤0.1)

The critical properties of perovskite manganite AMn_1−xGa_xO₃ (A=La_0.75Ca_0.08Sr_0.17, x=0, 0.05 and 0.1) at the ferromagnetic–paramagnetic transition have been analyzed. Experimental results revealed that all samples exhibit a second-order magnetic phase transition. The estimated critical exponents derived from the magnetic data using various techniques such as modified Arrott plot, Kouvel–Fisher method, and critical magnetization isotherms M(T_C, H). The critical exponent values for the undoped compound were found to match well with those predicted for the three-dimensional Heisenberg model (β=355±0.007, γ=1.326±0.002, δ=4.90±0.01). While on non-magnetic Ga substitution it tends towards mean-field with long-range interaction. The mean-field model might be due to the random dilution of the Mn sublattice by non-magnetic ion Ga³⁺ and/or the development of the physical size of the clusters which enhance the dipole–dipole interaction.     

Dielectric studies of phase transitions in the ferroelectric CdTiO3 and the Sr1−x CdxTiO3 solid solution

Temperature dependences of the permittivity and of the dielectric hysteresis loops in ceramic samples of nominally pure CdTiO₃ and a Sr_1?x Cd_xTiO₃ solid solution were studied. At 76.5±0.5 K, CdTiO₃ was established to undergo a ferroelectric phase transition close to the tricritical point. The temperature dependence of spontaneous polarization of CdTiO₃ is described within the Landau theory of phase transitions with the critical order parameter exponent ≈0.25. The phase diagram of the Sr_1?x Cd_xTiO₃ solid solution was drawn in (T, x) coordinates, and the critical concentration x _c =0.002, above which an induced polar state sets in the solid solution, was determined.     

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

A correlated majority model

We extend and solve analytically a bichromatic majority model including color correlation between nearest neighbor plaquettes. The behaviour of the one color, say black, dominant cluster size is studied as a function of the black concentration and the correlation degree. This mean value shows a divergence with a critical exponent v. We also define an order parameter m for the model whose critical exponent is β. We find v = β = 1 independent of the correlation degree. We present a Monte Carlo simulation of the process which gives a good agreement with the theoretical results.     

Ultrashort proton relaxation in one-dimensional TMMC doped by diamagnetic impurities

Proton spin-lattice relaxation rate has been measured at room temperature in impurity-doped TMMC: (CH₃)₄NMn_1?xCd_xCl₃ for x = 0.09 and 0.20. A drastic enhancement of the relaxation rate has been observed which is related to the behavior of the two-spin and four-spin correlation functions in linear short chains.     

AC susceptibility and intergranular critical current density study in pure and Ag doped (La1−xYx)2Ba2CaCu5Oz superconductors

The temperature and AC field amplitude variations of AC susceptibility have been measured on pure and 5 wt% Ag doped (La_1−xY_x)₂Ba₂CaCu₅O_z superconductors. The AC susceptibility as a function of field have been analyzed using Kim's critical state model. The temperature dependence of intergranular critical current density and the effective volume fractions of the grains have been estimated. The Ag doped samples show relatively large critical current density due to the improved intergranular coupling. The exponent of temperature variation of critical current density suggests that the weak links form superconductor-normal metal-superconductor (SNS) type of junctions for all the samples.     

Semi-infinite Ising model

For the semi-infinite Ising model in two or more dimensions, we prove analyticity properties of the surface free energy and map out the phase diagram in the absence of an external magnetic field. We prove that this phase diagram contains critical lines where the parallel and/or the transverse correlation lengths diverge. The critical exponent,v _⊥, of the transverse correlation length is shown to be equal to the exponentv of the Ising model on an infinite lattice. In a second paper, these results will be used to analyze the wetting transition.     

Height-height correlations for surface growth on percolation networks

The height-height correlations of the surface growth for equilibrium and nonequilibrium restricted solid-on-solid (RSOS) model were investigated on randomly diluted lattices, i.e., on infinite percolation networks. It was found that the correlation function calculated over the chemical distances reflected the dynamics better than that calculated over the geometrical distances. For the equilibrium growth on a critical percolation network, the correlation function for the evolution time t?1 yielded a power-law behavior with the power ζ^′, associated with the roughness exponent ζ via the relation ζ=ζ^′d_f/d_l, with d_f and d_l being, respectively, the fractal dimension and the chemical dimension of the substrate. For the nonequilibrium growth, on the other hand, the correlation functions did not yield power-law behaviors for the concentration of diluted sites x less than or equal to the critical concentration x_c.     

Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Demagnetisation effects in Fe3-xMnxSi alloys

Low field de susceptibility measurements have been made on an Fe_3-xMn_xSi alloy with x = 1.14. The observed and calculated results show a demagnetising effect to be occuring in and around the ferromagnetic regime. This brings into question earlier assertions of spin-glass or micromagnet like properties and the critical exponent estimates for these alloys because they lie within the region of significant demagnetisation.     

Vehicular traffic through a self-similar sequence of traffic lights

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self-similarly on a highway, where all traffic lights turn on and off simultaneously with cycle time T_s. The signals are positioned self-similarly by Cantor set. The nonlinear-map model of vehicular traffic controlled by self-similar signals is presented. The vehicle exhibits the complex behavior with varying cycle time. The tour time is much lower such that signals are positioned periodically with the same interval. The arrival time T(x) at position x scales as (T(x)-x)∝x^d_f, where d_f is the fractal dimension of Cantor set. The landscape in the plot of T(x)−x against cycle time T_s shows a self-affine fractal with roughness exponent α=1−d_f.