Calculation of critical exponents by self-similar factor approximants

Abstract

The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric phi^4 theory and of the Ising glass. It is demonstrated that this method, being much simpler than other known techniques of series summation in calculating the critical exponents, at the same time, yields the results that are in very good agreement with those of other rather complicated numerical methods. The principal advantage of the method of self-similar factor approximants is the combination of its extraordinary simplicity and high accuracy.

17 pages, 2 tables

References in corpus (10)

• The critical exponents of the superfluid transition in He4
• Principal problems in Bose-Einstein condensation of dilute gases
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
• Non-universal Critical Quantities from Variational Perturbation Theory and Their Application to the BEC Temperature Shift
• Extrapolation of power series by self-similar factor and root approximants
• Optimal trap shape for a Bose gas with attractive interactions
• Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors
• Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory
• Exact 1/N and Optimized Perturbative Evaluation of mu_c for Homogeneous Interacting Bose Gases

Cited by in corpus (12)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Physics of risk and uncertainty in quantum decision making
• Bose-Einstein-condensed gases in arbitrarily strong random potentials
• Self-similar factor approximants for evolution equations and boundary-value problems
• Bose systems in spatially random or time-varying potentials
• Optimization of self-similar factor approximants
• Order indices and entanglement production in quantum systems
• Self-similar extrapolation in quantum field theory
• Critical Temperature in Weakly Interacting Multicomponent Field Theory
• Critical correlations in an ultracold Bose gas revealed by means of a temporal Talbot-Lau interferometer
• Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit
• Population dynamics with nonlinear delayed carrying capacity