Self-consistent mean-field study of the anisotropic two-dimensional XY model

The self-consistent harmonic approximation is applied to the classical two-dimensional anisotropic XY (planar rotator) model on the square lattice. From the effective spin-wave stiffness constant data the phase diagram is constructed and the corresponding lattice dimensionally crossover exponents are defined and found. The variation of the stiffness constant jump with the anisotropy magnitude is obtained and the scaling functions ε(X) are extracted.     

Interpolating between Ising, XY-, and non-linear σ-models

The β-functions of O(N)-symmetric non-linear σ-models on the lattice were recently discovered to be non-monotonic for N 3. We explain the non-monotonic behaviour as a non-perturbative lattice effect by relating it to the Kosterlitz-Thouless transition of the XY-model. We also relate the latter transition to the phase transition of the Ising model. These relationships are established by interpolating between the O(N)- and the O(N − 1)-symmetric non-linear σ-models by suppression of the Nth component of the N-vector field with a mass term. A critical line in the coupling-mass plane connects the critical point of the Ising model (N = 1) with the critical point of the XY-model (N = 2). This line extends towards the region of non-monotonic behaviour of the β-function of the O(3)-symmetric model. The nature of the transition lines is also investigated.     

On the limit distribution of layer block spin variables in the mean spherical model

The limit distribution of the layer block spin variables of the mean spherical model under Neumann–Dirichlet boundary conditions is investigated in the presence of an inhomogeneous external field which changes sign at distance Lx (0x1) from the Neumann boundary. The behaviour of the equation of state is studied in different temperature and field regimes: high-temperature bulk limit, critical finite-size scaling regime, and low-temperature moderate-field regime. A new classes of critical behaviour for the characteristic function of the limit distributions are obtained and studied in the three different regimes.     

Short-time dynamics and critical behavior of three-dimensional bond-diluted Potts model

The short-time dynamics of the three-dimensional bond-diluted 4-state Potts model is investigated with Monte Carlo simulations. A recently suggested nonequilibrium reweighting method is applied, and the tricritical point is determined with the short-time dynamic approach. Based on the dynamic scaling form, both the dynamic and static critical exponents are estimated for the second order phase transition. Dynamic corrections to scaling are carefully considered.     

Scaling properties in temporal patterns of schizophrenia

Investigations into the patterns of schizophrenia reveal evidence of scaling properties in temporal behaviour. This is shown in the spectral properties of mid-range and long-range (up to two years) daily recordings from a sample of patients drawn at the therapeutic dwelling SOTERIA (Ambühl et al., in: Springer Series in Synergetics, Vol. 58, eds. Tschacher et al. (Springer, Berlin, 1992) pp. 195–203 and references therein) of the Psychiatric University Hospital in Bern. The therapeutic setting is unique in that it tries to avoid treatment by medication.

Power law behaviour has been found within fractal walk analysis and Fourier spectra for the daily fluctuations. A simple dynamic principle, based on a generic intermittency model, is put in relation to these time series thus predicting an additional scaling law for the distribution P(T) of time spans T between successive hospitalizations. Testing this hypothesis with our data shows only insignificant deviations. A possible role of this dynamic principle in the risk assignment of psychotic phases is explored with the help of an example.     

基于XY双变量特征提取策略的秸秆炭热值LIBS定量分析

农业生物质能已逐步成为我国现代工业主要清洁能源之一。利用激光诱导击穿光谱（LIBS）技术实现秸秆炭热值（CV）精准预测。针对传统X自变量特征提取方法在LIBS定量分析秸秆炭CV过程中缺陷问题,提出了一种XY双变量特征提取法。研究首先分析了秸秆炭CV与各元素含量之间相关性,选取与CV相关性极显著（p<0.01）的Y型特征变量,其主要获取了以炭单质、芳香环和羧基等形式存在的C,O,H和Na元素的分析线展宽波段;同时通过筛选偏最小二乘回归（PLSR）模型回归系数阈值获取与CV相关的X型特征变量,当阈值为4×10-5时模型交互验证均方根误差（RMSECV）降至最低值,其所对应的变量主要为参与农作物生理生长的Ca,Cr,Mg和K元素的分析线光谱线。基于所提取XY双特征变量构建遗传算法优化及自适应增强的人工神经网络（GA-BP-Adaboost）模型,当变异概率、交叉概率和相对误差率（RE）分别设为0.1,0.95和0.01时,最优模型预测平均相对误差（AREP）和预测相对标准误差（RSDP）分别为2.39%和2.97%,相比于XY-PLSR模型效果分别较低了0.82%和0.91%。结果表明：XY双变量特征提取法结合GA-BP-Adaboost模型可以为生物质炭在工业使用过程中CV精确定量预测分析提供方法依据。     

Reaching the unreachable: critical scaling at the superconducting transition

The large coherence length of conventional superconductors causes the critical region near T_c to be unobservably small, leading to the impression that mean-field theory can adequately explain properties near the transition. The high-temperature superconductors, however, have such strongly type-II character that the critical, or at least an intermediate critical, region is experimentally accessible. We demonstrate the applicability of XY-like critical scaling to magnetization, heat capacity and conductivity data and through the fitting parameters, make contact with a strong-coupling calculation of the critical temperature. Further, the scaled conductivity data show clear evidence for a thermodynamic transition along the freezing line H_m(T)∝(1 − T/T_c)^4/3.     

Short-time behavior of the kinetic spherical model with long-ranged interactions

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m₀ quenched from a very high temperature to T is solved. In the short-time regime, the bulk order increases with a power law in both the critical and phase-ordering dynamics. To the latter dynamics, a power law for the relative order is found in the intermediate time-regime. The short-time scaling relations of small m₀ are generalized to an arbitrary m₀ and all the time larger than . The characteristic functions for the scaling of m₀ and for are obtained. The crossover between scaling regimes is discussed in detail. Received 17 September 1999     

Transient anomalous dispersion in random walkers

A simple model of dispersive tracers which display a transient anomalous regime is presented. It is based on an ensemble of random walkers belonging to two independent populations characterized by different Lagrangian decorrelation times. Apart from short-time ballistic and long-time diffusive behavior, the dispersion shows anomalous scaling at intermediate times over a wide range of variability for the free parameters of the model.     

Consistency of optimizing finite-time Carnot engines with the low-dissipation model in the two-level atomic heat engine

The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation ΔS^(ir) on the operation time τ, i.e. ΔS^(ir) ∝ 1/τ. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the 1/τ-scaling. In this paper, we reveal that the optimization of the finite-time two-level atomic Carnot engines with the low-dissipation model is consistent only in the regime of η_C < 2(1 − δ)/(1 + δ), where η_C is the Carnot efficiency, and δ is the compression ratio in energy level difference of the heat engine cycle. In the large-η_C regime, the operation time for EMP obtained with the low-dissipation model is not within the valid regime of the 1/τ-scaling, and the exact EMP of the engine is found to surpass the well-known bound η₊ = η_C/(2 − η_C).     

Dynamic scaling behaviour of late-stage phase separation in Ni75AlxV25-x alloys

The dynamic scaling behaviour of late-stage phase separation and coarsening mechanisms of L12 and D022 in Ni75AlxV25-x （3 ≤ x ≤ 10, at.%） alloys are studied using the microscopic phase-field dynamic model. The microelaso ticity field is incorporated into the diffusion dynamic model. The results show the morphology and coarsening dynamics being greatly changed by the elastic interactions among different precipitates, the particles aligning along the dominant directions, the average domain size （ADS） of L12 and D022 deviating from the exponent of temporal power-law, and the growth slowing down due to the increasing of elastic interactions. The dynamic scaling regime of late-stage coarsening of the precipitates is attained. Thus the scaling behaviour of structure function is also applicable for elastic interaction systems. It is also found that the variations of ADS and scaling function depend on the volume fraction of precipitates.     

二层Ising模型的短时临界动力学性质

采用动力学Monte Carlo 方法研究了二层Ising模型的临界性质及早期动力学标度行为.结果表明层间耦合不为零时也存在临界点;计算了早期动力学临界指数θ;估计了传统的临界指数1/νz.其结果支持临界线存在的猜想,并表明此模型很可能是一种弱普适模型. 关键词：     

Monte Carlo and coarse graining renormalization studies for the XY model with cubic anisotropy

The XY model with cubic anisotropy is studied using a Monte Carlo coarse graining renormalization calculation. Particular emphasis is placed on the accuracy of phase diagrams and the finite-size effects on the phase transition. Non-universal behavior of the correlation-length critical exponent v with respect to variation of the cubic anisotropic field h₄ is analysed and an empirical formula v = [1 − exp(− ch₄)]⁻¹ is proposed. The results are discussed with reference to the surface reconstruction phase transition of the W(001) surface.     

Qualitative study of the boundary correlation function in the two-dimensional XY-model

The two-point correlation function at the rectilinear boundary of the two-dimensional half-space is studied for the XY-model for the case of free boundary conditions. It is shown that defects of vortex-type at the boundary form a one-dimensional plasma for T ≠ 0, but that this does not lead to exponential decay of the boundary correlation function for T < T_c^bulk.     

What does measure the scaling exponent of the correlation sum in the case of human heart rate?

It is shown that in the case of human heart rate, the scaling behavior of the correlation sum (calculated by the Grassberger-Procaccia algorithm) is a result of the interplay of various factors: finite resolution of the apparatus (finite-size effects), a wide dynamic range of mean heart rate, the amplitude of short-time variability being a decreasing function of the mean heart rate. This is done via constructing a simple model of heart rhythm: a signal with functionally modulated Gaussian noise. This model reproduces the scaling behavior of the correlation sum of real medical data. The value of the scaling exponent depends on all the above-mentioned factors, and is a certain measure of short-time variability of the signal.     

Short-time dynamics in the 1D long-range Potts model

We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r^1+σ. The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents θ' and z are derived in the cases q=2 and q=3 for several values of the parameter σ belonging to the nontrivial critical regime.     

Dynamic properties,scaling and related freezing criteria of two- and three-dimensional colloidal dispersions

The static and dynamic properties of 2- and 3-dimensional dispersions of strongly interacting colloidal spheres are examined. Quasi-2-dimensional dispersions of particles interacting by long range electrostatic and dipolar magnetic forces, respectively, are investigated using Brownian dynamics computer simulations with hydrodynamic interactions included. The dynamics of 3-dimensional bulk dispersions of charge-stabilized and neutral colloidal spheres is determined from a fully self-consistent mode-coupling scheme. For systems with long range repulsive interactions the dynamic correlation functions are shown to obey dynamic scaling in terms of a characteristic relaxation time related to the mean particle distance. Hydrodynamic interactions introduce a second characteristic length scale, and they lead to more restricted scaling behaviour with an enhancement of self-diffusion and, for 2-dimensional systems, to the divergence of the short-time collective diffusion coefficient. As a consequence of dynamic scaling, a dynamic criterion for the onset of colloidal freezing related to long-time self-diffusion is shown to be equivalent to a static freezing criterion related to the 2- and 3-dimensional static structure factors. Alternative freezing criteria are given in terms of the long-time and the mean collective diffusion coefficients.     

Thermodynamics of vortices in layered superconductors and the dependence of Tc on anisotropy

Data on multilayered superconductors such as YBa₂Cu₃O₇PrBa₂Cu₃O₇ show a strong dependence of T_c on anisotropy. In particular, the ratio T_cτ, where τ is the effective XY coupling constant, is found to vary by much more than the theoretical XY limit of 2.4. Layered superconductors allow for an additional anisotropy due to the core energy E_c of vortices perpendicular to the layers. It is shown that if E_c is large, such that the anisotropy is larger than exp(-E_cT_c), T_c is near a fluxon transition which is described by fluctuations of flux loops parallel to the layers. In the latter case T_cτ can vary by more than 2.4, accounting for the data.     

On the rotational partition function for tetrahedral molecules

A rigorous calculation of the quantum-mechanical rotational partition function for tetrahedral XY₄ molecules yields Q_r = ( )(2I_Y + 1)⁴π ^- exp(/4), where I_Y is the spin of the Y nucleus, and ≡ Bhc/kT. This result is accurate to 1 per cent or better for all values of B and T such that < .     

Non-universal critical behaviour of heteronuclear dimers on a square lattice––A Monte Carlo study

Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u_BB=u_AB=−1, and for non-repulsive energy between AA nearest-neighbour sites, u_AA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when u_AA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of u_AA.