Some Observations on the Early History of Equilibrium Statistical Mechanics

The article begins with some personal comments by the author on the outstanding contributions of Michael Fisher to statistical mechanics and critical phenomena. Its major aim is to trace the contributions of a number of pioneering personalities to the early history of equilibrium statistical mechanics. Four different areas are considered: (1) Classical Statistical Mechanics, (2) Quantum Statistical Mechanics, (3) Interacting Systems, and (4) The Ising Model. The article is concerned with the development and applications of statistical mechanics when certain basic assumptions are made. It does not deal with the justification of these assumptions which is a sophisticated discipline of its own.     

Gauge-invariant lattice gas for the microcanonical Ising model

We introduce a lattice gas for particles with discrete momenta (1, 0, –1) and local deterministic microdynamics, which exactly reproduces Creutz's microcanonical algorithm for the ferromagnetic Ising model. However, because of the manifest gauge invariance of our variables, both the Ising ferromagnetic and spin-glass systems share precisely the same dynamics with different initial conditions. Additional conservation laws in the 1D Ising case result in a completely integrable system in the limit of zero or unbounded demon energy cutoff. Numerical investigations of ergodicity are presented for the pure Ising lattice gas in one and two dimensions.     

Critical Exponents of the Diluted Ising Model between Dimensions 2 and 4

Within the massive field-theoretic renormalization-group approach the expressions for the and functions of the anisotropic mn-vector model are obtained for general space dimension d in three-loop approximation. Resumming corresponding asymptotic series, critical exponents for the case of the weakly diluted quenched Ising model (m = 1, n = 0), as well as estimates for the marginal order parameter component number m _c of the weakly diluted quenched m-vector model, are calculated as functions of d in the region 2 d < 4. Conclusions concerning the effectiveness of different resummation techniques are drawn.     

Monte Carlo study of the critical behavior of pure and site-diluted Ising ferro-and ferrimagnets

Monte Carlo simulations are performed for pure and site-diluted Ising ferro- and ferrimagnets on a simple cubic lattice with up to 40³ sites and with impurity concentrationx. For the diluted ferromagnet (x=0.2) the exponent= 0.392±0.03 is definitely larger than the pure model value of=0.304±0.03. In contrast, for ferrimagnetic systems (x=0, 0.1, 0.2) the values appear to be independent ofx and within the error limits consistent with the value for the pure ferromagnet, possibly because the width of the asymptotic random critical regime (or of the crossover regime) is even smaller than in the case of ferromagnets.     

Restrictions on the phase diagrams for a large class of multisite interaction spin systems

Through the proof of two very general theorems involving Ising spin systems with multisite interactions, specific regions of the complexh plane, whereh is the external magnetic field, are shown to be free of zeros of the partition function. Hence in these regions the partition function is analytic and phase transitions are absent. As an example: for systems with ferromagnetic multisite interactions involving even numbers of sites, no phase transition occurs outside of an interval centered on the origin of the realh axis and of the form (–C(T),C(T)), whereT is the temperature. For T0,C(T)0 and phase transitions can occur only ath=0.     

Phase diagrams of Ising models on Husimi trees II. Pair Wand multisite interaction systems

We continue an earlier study of multisite interaction Ising spin models on Husimi trees. In particular, attention is given to systems with both a nearestneighbor pair interaction and three-site interactions. We use our calculations of the phase diagrams of the systems on Husimi trees as approximations of systems with the same interactions but on a regular lattice, e.g., the triangle lattice. Specific models where exact results are available are used as test cases. All of the work involves computation of quantities, such as the magnetization, by iterative processes. Hence we are dealing with a discrete map and for certain values of the interaction strengths we obtain for the magnetization diagram results involving period doubling, chaos, period-three windows, etc., all phenomena of recent interest in connection with dynamical systems and now associated with certain Ising spin systems.     

Critical exponents of random Ising-like systems in general dimensions

Critical exponents of weakly dilute Ising-like systems are computed for non-integer space dimensionalities in the range 2</d4. The calculations are performed in the framework of the Callan-Symanzik field-theoretic approach. Two-loop renormalization group functions are obtained as renormalized perturbation theory series expansions directly in noninteger dimensions. The values of the critical exponents are estimated with the use of the two-variable Borel resummation method.     

Discovering Noncritical Organization: Statistical Mechanical,Information Theoretic,and Computational Views of Patterns in One-Dimensional Spin Systems

We compare and contrast three different, but complementary views of “structure” and “pattern” in spatial processes. For definiteness and analytical clarity, we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions. These noncritical systems are well-suited for this study since the change in structure as a function of system parameters is more subtle than that found in critical systems where, at a phase transition, many observables diverge, thereby making the detection of change in structure obvious. This survey demonstrates that the measures of pattern from information theory and computational mechanics differ from known thermodynamic and statistical mechanical functions. Moreover, they capture important structural features that are otherwise missed. In particular, a type of mutual information called the excess entropy—an information theoretic measure of memory—serves to detect ordered, low entropy density patterns. It is superior in several respects to other functions used to probe structure, such as magnetization and structure factors. ϵ-Machines—the main objects of computational mechanics—are seen to be the most direct approach to revealing the (group and semigroup) symmetries possessed by the spatial patterns and to estimating the minimum amount of memory required to reproduce the configuration ensemble, a quantity known as the statistical complexity. Finally, we argue that the information theoretic and computational mechanical analyses of spatial patterns capture the intrinsic computational capabilities embedded in spin systems—how they store, transmit, and manipulate configurational information to produce spatial structure.     

On Decay of Correlations for Unbounded Spin Systems with Arbitrary Boundary Conditions

We propose a method based on cluster expansion to study the truncated correlations of unbounded spin systems uniformly in the boundary condition and in a possible external field. By this method we study the spin–spin truncated correlations of various systems, including the case of infinite range simply integrable interactions, and we show how suitable boundary conditions and/or external fields may improve the decay of the correlations.     

Hierarchical neural networks for the storage of correlated memories

A class of hierarchical neural network models introduced by Dotsenko for the storage and associative recall of strongly correlated memories is studied analytically and numerically. In these models, patterns stored in higher levels of the hierarchy represent generalized categories and those stored in lower levels describe finer details. We first show that the models originally proposed by Dotsenko have a serious flaw: they are not able to detect or correct errors in categorization which may be present in the input. We then describe three different models which attempt to overcome this shortcoming of the original models. In the first model, the interaction between different levels of the hierarchy has the form of an external field conjugate to memories stored in the lower level. In the second model, a three-spin interaction term is included in addition to the usual binary interactions of the Hopfield type. The third model makes use of a time delay mechanism to induce, if necessary, transitions between memory states and their complements. Detailed analytical and numerical studies of the performance of these models are presented. Our analysis shows that all three models are able to detect and also to correct in varying degrees any error in categorization that may be present in the input pattern.     

Convergence to Equilibrium of Random Ising Models in the Griffiths Phase

We consider Glauber-type dynamics for disordered Ising spin systems with nearest neighbor pair interactions in the Griffiths phase. We prove that in a nontrivial portion of the Griffiths phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1. This condition has, in turn, been shown elsewhere to imply that the convergence to equilibrium is faster than any stretched exponential, and that the average over the disorder of the time-autocorrelation function goes to equilibrium faster than exp[–k(log t) ^d/(d–1)]. We then show that for the diluted Ising model these upper bounds are optimal.     

A Review of Technological Forecasting from the Perspective of Complex Systems

Technology forecasting (TF) is an important way to address technological innovation in fast-changing market environments and enhance the competitiveness of organizations in dynamic and complex environments. However, few studies have investigated the complex process problem of how to select the most appropriate forecasts for organizational characteristics. This paper attempts to fill this research gap by reviewing the TF literature based on a complex systems perspective. We first identify four contexts (technology opportunity identification, technology assessment, technology trend and evolutionary analysis, and others) involved in the systems of TF to indicate the research boundary of the system. Secondly, the four types of agents (field of analysis, object of analysis, data source, and approach) are explored to reveal the basic elements of the systems. Finally, the visualization of the interaction between multiple agents in full context and specific contexts is realized in the form of a network. The interaction relationship network illustrates how the subjects coordinate and cooperate to realize the TF context. Accordingly, we illustrate suggest five trends for future research: (1) refinement of the context; (2) optimization and expansion of the analysis field; (3) extension of the analysis object; (4) convergence and diversification of the data source; and (5) combination and optimization of the approach.     

Existence of the thermodynamic limit in nonequilibrium systems

The existence of a thermodynamic limit in nonequilibrium stochastic and quantal systems is proven for finite-range interactions and macrovariables which are bounded in the sense of norm. This condition is easily confirmed to be satisfied for specific models, such as the kinetic Ising model and quantal spin systems.Partially financed by Japanese Scientific Research Fund of the Ministry of Education.     

A Novel Method for Vibration Mitigation of Complex Mechanical Systems

Taking the complex mechanical systems as the research project, a theoretical multi-degree-of-freedom (MDOF) model was established. Based on the vibration characteristics analysis of this system, a novel method of vibration mitigation was proposed, which can be applied to most of the complex mechanical systems. Through this method, limited grounding stiffness was made use of and added to certain degree of freedom (DOF) discretely. Thus, the root-meansquare (RMS) of the systems amplitude can be reduced to ideal level. The MATLAB code based on this method was attached, which was tested on the theoretical model. Consider that complex mechanical systems are nonlinear and uncertain, theoretically the optimal solution of vibration mitigation is inaccessible. However, this method can always provide a relatively effective solution.     

含ZnO样本集晶格匹配和热匹配的模式识别分析

利用动态聚类分析、最小生成树、主成分分析等模式识别方法,对含ＺｎＯ半导体材料的样本集中各样本之间在３００Ｋ时的晶格匹配与热匹配程度进行了分析。结果表明：在３００Ｋ时,三种Ⅲ－Ⅴ族氮化物ＡｌＮ、ＧａＮ、ＩｎＮ与ＺｎＯ材料之间的晶格匹配和热匹配程序最好。由最小生成树以及主成分二维映射结果可知两类样本分区明显,分类效果良好,表明利用模式识别方法可对含ＺｎＯ样本集中各样本之间的晶格匹配和热匹配程度进行识别     

用于光学系统分析的质心配准法

将图像区域像素的统计特征引入活动轮廓模型,提出使分割轮廓所包括区域的质心对应角均方根误差极小的最优搜索方法——质心配准法。质心配准法有效地避免了散斑噪声等图像污染对图像区域分割精度的影响,实现了模糊图像精确的区域分割,求得图像最佳配准参数。对实际光学系统输出的多幅具有较大空时互补性的低分辨率图像进行了仿真实验,实验结果表明：该配准算法具有较高的精度,并在光学系统分析上得到了很好的应用。     

拉曼光谱结合模式识别方法用于大豆原油掺伪的快速判别

大豆原油是我国的战略储备物资,然而目前储油市场上频繁出现大豆原油掺混的现象严重影响了食用油储备安全。基于此,通过大豆原油与部分植物精炼油拉曼谱图的特征差异,并结合主成分分析-支持向量机(PCA-SVM)模式识别建立了大豆原油是否掺伪的快速判别方法。以28个大豆原油、46个精炼油、110个掺伪油的拉曼谱图为模型样本;选择位于780～1 800 cm-1波段的谱图,预处理方法同时采用Y轴强度校正、基线校正和谱图归一化法;在此基础上应用PCA法提取特征变量,即以贡献率最高前7个主成分为变量进行SVM分析。SVM校正模型的建立是以随机选取的20个大豆原油和75个掺伪油样组成校正集,以8个大豆原油和35个掺伪油样组成验证集,分别运用并比较四种核函数算法建立的大豆原油SVM分类模型,并采用网格搜索法(grid-search)优化模型的参数,以四种模型的分类性能作为评判标准。结果表明：应用线性核函数算法构建的SVM分类模型可以很好地完成掺伪大豆原油的判别,校正集识别准确率达到100%,预测结果的误判率为0,判别下限为2.5%。结果表明应用拉曼光谱结合化学计量学能够用于大豆原油掺伪的快速鉴别。拉曼光谱简便、快速、无损、几乎没有试剂消耗,适合现场检测,从而为大豆原油的掺伪分析提供了一种新的备选方法。     

The Phase Diagram of the Quantum Curie-Weiss Model

This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the model in the parameters of inverse temperature and transverse field strength. Further analysis computes the critical exponent for the vanishing of the order parameter in the approach to the critical curve and gives useful stability properties for a variational problem associated with the representation.     

Behavior of the effective fields for a regular ising model on the Cayley tree

A regular Ising model with nearest-neighbor interactions ofJ and–J(J>0) on a Cayley tree of coordination number 3 is investigated for the behavior of effective fields in a uniform external field. The effective fields show periodic and also aperiodic structures in the temperature-field plane. At absolute zero temperature, the equations determining effective fields are reduced to a nonlinear, one-dimensional, iterative equation. Arithmetic furcations of period and a screening of the furcations are observed.     

基于近红外光谱法的多组分复杂溢油源定量建模分析

研究利用近红外光谱分析方法进行模拟复杂混合溢油源的定量分析问题。选取汽油、柴油、煤油三种轻质石油类产品,按照不同浓度比例配置成40个模拟混合溢油样本,利用傅里叶变换近红外光谱仪采集其在4 000～12 000 cm-1谱区范围内的近红外光谱;采用不同预处理方法,利用偏最小二乘算法建立混合溢油样本三组分各自的浓度定量模型。汽油、柴油和煤油的最优预处理方法均为二阶导数方法,分别在8 501.3～7 999.8 cm-1,6 102.1～4 597.8 cm-1,6 549.5～4 597.8 cm-1,7 999.8～7 498.4 cm-1和6 102.1～4 597.8 cm-1谱区范围内,预测模型的决定系数R2分别为0.998 2,0.990 2和0.993 6;RMSEP值分别为0.474 7,0.936 1和1.013 1;RPD值分别为25.126 9,10.517 3和13.072 0。实验结果表明：利用近红外光谱分析技术结合化学计量学方法能够定量确定模拟混合溢油样本中各组分的浓度,为海洋复杂溢油源的定量检测与分析提供有效手段。