Critical Indices as Limits of Control Functions

Details Critical Indices as Limits of Control Functions Critical Indices as Limits of Control Functions

1997-08-16

arxiv.org/abs/cond-mat/9708120v1

Phys. Rev. Lett. 79 (1997) 333-336

Physics

Condensed Matter

Statistical Mechanics

1 file, 5 pages, RevTex

Scientific paper

10.1103/PhysRevLett.79.333

A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the role of control functions governing the fastest convergence of the renormalized series. A striking relation between the theory of critical phenomena and optimal control theory is discovered: The critical indices are found to be directly related to limits of control functions at critical points. The method is applied to calculating the critical indices for several difficult problems. The results are in very good agreement with accurate numerical data.

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