Finite-Size Scaling Theory
Finite-Size Scaling Theory
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有限尺寸缩放理论
DOI：
10.1142/9789814503419_0001
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
V. Privman
中科院分区：
文献类型：
--
作者：
V. Privman
包括以下部分：结构简介打开注释综述概述基本标度假设临界点FINITE尺寸标度RG的标度因子和标度的修正极限尺寸标度度规因子的选择非周期边界条件表面和角点自由能系统的有限尺寸特性其他研究主题微观正则和固定系谱各向同性模型动力学随机系统展开结果CRITAL点标度：自由能量和标度长度的高阶自由能比和相关长度的ϵ导数模型结果的调查自由能和尺度长度的三维尺度估计的形式上的Binder积累量表面(边界条件)结果结果有角体系二维自由能标度自由能幅值对界面性能的SIZE效应临界点附近界面自由能周期性界面的理论和数值结果周期界面钉扎界面二维计算结果钉扎界面自由能低于临界点其他研究课题圆柱体和板条几何尺寸对湿润的影响圆柱体和板条几何形状中浮动界面尺寸效应一阶自由能阶跃温度附近自由能阶跃变温度附近自由能阶跃一阶跨尺度一阶跨立方伊辛模型在边界相夸克近似下的三次伊辛模型Néel超参平均场理论中的连续性巨型自旋概念和定点尺度计算一阶跃迁界面的上临界尺寸与柱面几何的ξ‖尺度极限的纵向关联圆柱和立方体圆柱极限标度的自旋波效应立方几何中的自旋波球模型结果量子模型非对称跃迁一般公式两相共存序参数的概率分布精确和传递矩阵结果其他主题标度公式的匹配扩展到非周期边界条件配分函数零点的轨迹结论认识参考文献
The following sections are included:INTRODUCTIONOpening RemarksOutline of the ReviewBasic Scaling PostulateFINITE-SIZE SCALING AT CRITICAL POINTSScaling Ansatz forRG and Corrections to ScalingFinite-Size Scaling in the LimitSelection of Metric FactorsNonperiodic boundary conditionsSurface and Corner Free EnergiesFinite-Size Properties ofsystemsOther Research TopicsMicrocanonical and Fixed-EnsemblesAnisotropic ModelsDynamicsRandom SystemsCRITICAL-POINT SCALING: SURVEY OF RESULTSDefinitions and NotationThermodynamic QuantitiesBinder's Cumulant RatioTypes of Surfaces (Boundary Conditions)Results for Cumulant and Other RatiosBinder's Cumulant Ratio at TcCumulant Scaling AsymptoticsHigh-Order Free Energy Derivative Ratios at TcFree Energy and Correlation Length ScalingSpherical Model Resultsϵ-Expansion ResultsNumerical Estimates of 3d AmplitudesConformal Invariance in 2dCorrelation Lengths forstripsSecond-Moment Correlation Length Amplitudes in2dTests of Free Energy Scaling in2dFree Energy Amplitudes for Systems with CornersSIZE EFFECTS ON INTERFACIAL PROPERTIESInterfacial Free Energy Near CriticalityPeriodic InterfacesExact and Numerical Results for Periodic InterfacesPinned InterfacesExact 2dIsing Results for Pinned InterfacesInterfacial Free Energy Below CriticalityOther Research TopicsSize Effects on WettingFluctuating Interfaces in Cylindrical and Slab GeometriesStep Free Energy Near Roughening TemperatureFIRST-ORDER TRANSITIONSOpening RemarksHypercubic Ising Models at the Phase BoundaryCubicn-Vector Models in the Giant-Spin ApproximationNéel's Mean-Field Theory of SuperparamagnetismGiant-Spin Concept and Discontinuity Fixed Point ScalingUpper Critical Dimension for First-Order TransitionsCrossover to Cylindrical Geometry: Ising CaseLongitudinal Correlation LengthCalculation of the Scaling FunctionsCylindrical Limit ScalingSize Dependence of ξ‖and RG ScalingExact and Numerical Tests of Scaling for Ising Cylinders and CubesSpin-Wave Effects forCylinder-Limit ScalingSpin Waves in Cubic GeometriesSpherical Model ResultsQuantum ModelsNonsymmetricTransitionsGeneral FormulationTwo-Phase CoexistenceProbability Distribution for the Order ParameterExact and Transfer Matrix ResultsMiscellaneous TopicsMatching of Scaling FormsExtension to Nonperiodic Boundary ConditionsLoci of Partition Function ZerosConclusionAcknowledgementsREFERENCES