50 years of Yukhnovskii's critical point theory: its place in the constant flow of theoretical physics

TL;DR

This paper reviews Ihor Yukhnovskii's 50-year-old critical point theory for the 3D Ising model, highlighting its historical significance, methodological innovation, and its place within the broader development of quantum field theory and statistical physics.

Contribution

It provides a comprehensive analysis of Yukhnovskii's layer-by-layer integration method and its impact on the evolution of critical phenomena theories over the past five decades.

Findings

Yukhnovskii's method offers deeper insights into critical phenomena.

His approach is an alternative to Wilson's epsilon-expansion.

The theory has influenced developments in quantum field theory and statistical physics.

Abstract

Half a century ago, Ihor Yukhnovskii elaborated a method of studying the critical point of the three-dimensional Ising model based on a layer-by-layer integration in the space of collective variables. His method was an alternative to that based on the $\varepsilon$-expansion for which K. G. Wilson was awarded the Nobel Prize in Physics in 1982. However, Yukhnovskii's technique, which yielded similar results, provided even deeper insight into the nature of this phenomenon. At that time, we, professor's students, saw only this aspect of his theory. Later, I realized that the mentioned Yukhnovskii's work naturally fits into a more general context of the turbulent development of quantum field theory and statistical physics in the last quarter of the twentieth century. The aim of the present article is to look at the main aspects and the impact of Yukhnovskii's theory from this perspective.