Algebraic Self-Similar Renormalization in Theory of Critical Phenomena

TL;DR

This paper introduces an optimized self-similar renormalization method for accurately calculating critical temperatures and indices in critical phenomena, demonstrating its effectiveness through various examples.

Contribution

The paper proposes a new optimized variant of the self-similar renormalization method for better summation of asymptotic series in critical phenomena.

Findings

High accuracy in calculating critical temperatures and indices

Effective summation of asymptotic series demonstrated

Method combines simplicity with precision

Abstract

We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several different examples. The advantage of the method is in combining simplicity with high accuracy.