On finite-size scaling of the order parameter in percolation

Finite-size scaling of the order parameter O in the disordered phase is presented for percolation in 2d and 3d and compared to the behavior of the magnetization of the Ising model. We find that the order parameter O grows logarithmically with the system size L for p < p_c and thus the analogy with the Ising model is not complete. Furthermore we find evidence for scaling behavior of the type O ～ L^?y/v (p_c ? p)^β?y where the exponent y is not dv/2 as in the Is ing case.     

Size-driven dimensional crossover in the quasi-two-dimensional Ising model

We have studied the finite size effect in the quasi-two-dimensional Ising model by using a Monte Carlo simulation. A marked finite size effect was found with decreasing interlayer interaction. Aside from the well-known three- to two-dimensional crossover, a three- to one-dimensional crossover at a crossover size L_c∼(λ/2)^−ν/φ was revealed as an origin of the marked finite size effect, where λ is the interlayer to intralayer interaction ratio, and ν and φ are the critical exponent for the correlation length and the crossover exponent, respectively. While the former crossover is driven by temperature, the latter is driven by size at a fixed λ.     

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.     

Structure and high pressure behaviour of organic crystals based on aromatically substituted 1,3,4-oxadiazoles

The crystalline structure of a new compound containing the 1,3,4-oxadiazole moiety, 4-(5-methyl-1,3,4-oxadiazole-2yl-)-N,N′-dimethyl-phenylamine (MODPA) was determined. It shows a monoclinic structure with space group P2₁/c and lattice parameters: a=1.02997(6), b=0.64840(4), c=1.58117(10) nm and β=99.4820(10)°. To study the intermolecular interactions in oxadiazole containing organic crystals, X-ray studies on MODPA and 2,5-diphenyl-1,3,4-oxadiazole (DPO) were performed up to 5 GPa at room temperature. The Murnaghan equation of state is used to describe the compression behaviour of both substances. From these results, the bulk modulus and its pressure derivative were determined. The values obtained are: K₀=6.3 GPa and K′₀=6.8 for MODPA and K₀=7.3 GPa and K′₀=6.7 for DPO. Additionally, measurements under increasing temperature at ambient pressure were carried out to evaluate the thermal expansion coefficient: α=1.8×10⁻⁴ K⁻¹ for MODPA and α=1.9×10⁻⁴ K⁻¹ for DPO.     

Thermodynamics of the quantum and classical Ising models with skew magnetic field

The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for |J|β?0.9, is derived for the ferromagnetic and antiferromagnetic cases. The high-temperature expansion (β-expansion) of the Helmholtz free energy is calculated up to order β⁷ for the quantum version (spin S≥1/2) and up to order β¹⁹ for the classical version. In contrast to the S=1/2 case, the thermodynamics of the transverse Ising and that of the XY model for S>1/2 are not equivalent. Moreover, the critical line of the T=0 classical antiferromagnetic Ising model with skew magnetic field is absent from this classical model, at least in the temperature range of |J|β?0.9.     

n维格子上Ising模型临界温度的上界

本文利用耦合的技巧,建立了Ising模型与接触过程的联系。由此给出了Ising模型临界温度的上界,即n维Ising模型的临界点β_c(n)应满足 exp{2β_c(n)(2n-1)}·(exp{2β_c(n)}-1)≥2/2n-1。特别是三维Ising模型的临界点β_c(3)>1/2ln1.17。 关键词：     

Perturbation calculations for the eight-vertex model around the Ising point for T → Tc+. II

The dispersion expansion for the two-point electric correlation function in the eight-vertex model is calculated to first order in the four-spin coupling in the scaling limit in the high-temperature regime. It is found that there is a close relation between the T_c⁻ and T_c⁺ spin-spin-energy density correlation function in the Ising model. This is used to simplify tremendously the calculation in the T_c⁺ case; the result can be obtained from the T_c⁻ result by deleting two variables in the expansion.     

Characterization of polycrystalline (Na,K)β/β′- alumina ceramics

K β′-alumina is unstable at >1300°C. Mixed alkali β′-alumina has a variable stability depending on the alkali ratio, [K⁺]/([Na⁺]+[K⁺]). For f(β)<[K⁺]/([Na⁺]+[K⁺]), the β′-Al₂O₃ phase decomposes to Kβ-Al₂O₃ 0997 0815 V 3 and a solid solution of Na β′-Al₂O₃ and K β′-Al₂O₃. For f(β)=[K⁺]/([Na⁺]+[K⁺], the ceramic consists of K β-Al₂O₃ and Naβ′-Al₂O₃ and for f(β)>[K⁺]/([Na⁺]+[K⁺]), the excess Na⁺ after Na β′-Al₂O₃ dissolves in the β phase, giving Na β-Al₂O₃/K β-Al₂O₃ solid solution and Na β′-Al₂O₃. These sequences were confirmed by measuring the dependence of the c-axis lattice parameters of β- and β′-Al₂O₃ phases on the f(β), and the change of these parameters during the ion-exchange of Na⁺ and K⁺ ions.     

The bulk modulus of SmFeAs(O0.93F0.07)

The crystal structure of SmFeAs(O_0.93F_0.07) has been investigated under high pressure (up to ∼9 GPa) by means of synchrotron powder diffraction analysis followed by Rietveld refinement. The bulk modulus was calculated (K₀ = 103 GPa) using a 3rd order Birch–Murnaghan equation of state and resulted in quite good agreement with theoretical calculations reported for LaFeAsO. The linear compressibilities β_a and β_c are 2.11(4) and 4.56(7) × 10⁻³ GPa⁻¹, respectively.     

Comment on the real part of the K±p forward scattering amplitude

It is observed that the K_L⁰n→K_S⁰n regeneration measurements require positivity of the real part of the K^?p forward scattering amplitude above p ～ 1.3 GeV/c. This invalidates some of the earlier dispersion relation predictions and the preliminary experimental results from Batavia.     

Etude par effet Mössbauer de Ca2MnO4 dope a l'etain

The antiferromagnetic layer phase Ca₂MnO₄ doped with ¹¹⁹Sn⁴⁺ has been investigated by Mössbauer spectroscopy. Below the Néel temperature a hyperfine magnetic field transfered on the tin nucleus is observed with saturation value H(0)?38 kOe. The low value of the transfered field is attributed to the absence of e_g electrons on the 3d orbitals of Mn⁴⁺. Supposing the field to follow the power law H(T) = H(0)D[1 ? (T/T_N)]^β as the sublattice magnetizations usually do, the study of the temperature dependence of the field yields β = 0.44 ± 0.10. This value for the critical exponent is in rather good agreement with the value deduced from neutron measurements (β = 0.38 ± 0.06) as well as with those calculated from three dimensional Heisenberg and Ising models (0.31?β?0.38). It is anyway very different from the theoretical value for a two dimensional Ising model (β = 0.125) and from the experimental values for various two-dimensional antiferromagnets isostructural with Ca₂MnO₄ such as K₂MnF₄ (β = 0.15) or K₂NiF₄ (β = 0.14).     

Calculation of critical properties for the anisotropic two-layer Ising model on the Kagome lattice: Cellular automata approach

The critical point (K_c) of the two-layer Ising model on the Kagome lattice has been calculated with a high precision, using the probabilistic cellular automata with the Glauber algorithm. The critical point is calculated for different values of the inter- and intra-layer couplings (K₁≠K₂≠K₃≠K_z), where K₁, K₂ and K₃ are the nearest-neighbor interactions within each layer in the 1, 2 and 3 directions, respectively, and K_z is the intralayer coupling. A general ansatz equation for the critical point is given as a function of the inter- and intra-layer interactions, ξ=K₃/K₁,σ=K₂/K₁ and ω=K_z/K₁ for the one- and two-layer Ising models on the Kagome lattice.     

Dynamics of the one-dimensional random transverse Ising model with next-nearest-neighbor interactions

The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the case of bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the case of Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as K_i increase, especially when K_i>J_i/2 (J_i and K_i are the exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak (K_i<J_i/2).     

On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Boundary Conditions at Low Temperature

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to ?). For β large enough we show that for any ${\varepsilon >0 }We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to −). For β large enough we show that for any ${\varepsilon >0 }${\varepsilon >0 } there exists c=c(b,e){c=c(\beta,\varepsilon)} such that the corresponding mixing time T _mix satisfies lim_L?￥ P(T_mix 3 exp(cL^e)) = 0{{\rm lim}_{L\to\infty}\,{\bf P}\left(T_{\rm mix}\ge {\rm exp}({cL^\varepsilon})\right) =0}. In the non-random case τ ≡ +  (or τ ≡ −), this implies that T_mix ￡ exp(cL^e){T_{\rm mix}\le {\rm exp}({cL^\varepsilon})}. The same bound holds when the boundary conditions are all +  on three sides and all − on the remaining one. The result, although still very far from the expected Lifshitz behavior T _mix = O(L ²), considerably improves upon the previous known estimates of the form T_mix ￡ exp(c L^{\frac 12 + e}){T_{\rm mix}\le {\rm exp}({c L^{\frac 12 + \varepsilon}})}. The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

Ising ferromagnet with biquadratic exchange

A spin one Ising system with biquadratic exchange, is investigated, using Green's function technique in random phase approximation (RPA). Transition temperature T_c and <(S^z)²> at T_c, are found to increase with biquadratic exchange parameter α for sc, bcc and fcc lattices. The variation of <(S^z)²> at T_c with α is found to be the same for the above lattices.     

Dynamic hysteresis of magnetic aggregates with non-integer dimension

We investigate the dynamic hysteresis of nanoscale magnetic aggregates by employing Monte Carlo simulation, based on Ising model in non-integer dimensional space. The diffusion-limited aggregation (DLA) model with adjustable sticking probability is used to generate magnetic aggregates with different fractal dimension D. It is revealed that the exponential scaling law A(H₀, ω)∼H₀^α·ω^β, where A is the hysteresis area, H₀ and ω the amplitude and frequency of external magnetic field, applies to both the low-ω and high-ω regimes, while exponents α and β decrease with increasing D in the low-ω regime and keep invariant in the high-ω regime. A mean-field approach is developed to explain the simulated results.     

Thermodynamic geometry of a kagome Ising model in a magnetic field

We derived the thermodynamic curvature of the Ising model on a kagome lattice under the presence of an external magnetic field. The curvature was found to have a singularity at the critical point. We focused on the zero field case to derive thermodynamic curvature and its components near the criticality. According to standard scaling, scalar curvature R   behaves as |β−_βc|^α−2${|\beta -{\beta }_c|}^{\alpha -2}$ for α>0$\alpha >0$ where β is the inverse temperature and α is the critical exponent of specific heat. In the model considered here in which α is zero, we found that R   behaves as |β−_βc|^α−1${|\beta -{\beta }_c|}^{\alpha -1}$.