Self-Similar Crossover in Statistical Physics

Abstract

An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar approximation theory, being its variant where control functions are defined from asymptotic crossover conditions. Several examples from statistical physics demonstrate that the suggested method results in rather simple and surprisingly accurate formulae.

1 file, 23 pages, LaTex

References in corpus (5)

• Temporal Dynamics in Perturbation Theory
• Self-Similar Interpolation in Quantum Mechanics
• Critical Indices as Limits of Control Functions
• Self-Similar Bootstrap of Divergent Series
• Algebraic Self-Similar Renormalization in Theory of Critical Phenomena

Cited by in corpus (9)

• Summation of Power Series by Self-Similar Factor Approximants
• Self-Similar Structures and Fractal Transforms in Approximation Theory
• Extrapolation of power series by self-similar factor and root approximants
• Self-similar factor approximants for evolution equations and boundary-value problems
• Classification of Possible Finite-Time Singularities by Functional Renormalization
• Self-similarly corrected Pade approximants for nonlinear equations
• Low-Temperature Properties of Ferromagnetic Spin Chains in a Magnetic Field
• Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction
• Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions