Statistical Mechanical Theory of Cooperative Phenomena.I.General Theory of Fluctuations,Coherent Anomalies and Scaling Exponents with Simple Applications to Critical Phenomena
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A general method is proposed to study non-classical scaling behaviors ofcooperative systems. This is based on the appearance of a "coherent anomaly" inmean-field-type or classical approximations of cooperative systems. The degree of ap-proximation is analytically continued to construct a parameterized expression of awhole set of approximations, using Kubo's linear response theory. General relationsbetween scaling (or critical) exponents and "coherent-anomaly' exponents" are deriv-ed using the theory of envelope and are also obtained from a finite-degree-of-approx-imation scaling, which is inspired by Fisher's finite-size scaling. The present coherent-anomaly method (CAM) is promising for calculating analytically non-classical scal-ing exponents in cooperative phenomena. A general scheme of CAM in criticalphenomena is presented. It is shown that even the combination of the Weiss andBethe approximations gives rather good estimates of static and dynamic critical ex-ponents.
- 社団法人日本物理学会の論文
- 1986-12-15
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