Critical Exponents without beta-Function

TL;DR

This paper demonstrates that critical exponents can be derived using strong-coupling theory without relying on the beta-function, simplifying the analysis of critical phenomena.

Contribution

It introduces a method to compute main critical exponents solely from two renormalization constants, eliminating the need for the beta-function.

Findings

Critical exponents nu, eta, omega can be calculated without the beta-function.

The renormalization constant of the coupling strength is unnecessary for these calculations.

The approach simplifies the theoretical framework for analyzing critical phenomena.

Abstract

We point out that the recently developed strong-coupling theory enables us to calculate the three main critical exponents nu, eta, omega, from the knowledge of only the two renormalization constants Z_phi of wave function and Z_m of mass. The renormalization constant of the coupling strength is superfluous, and with it also the beta-function, the crucial quantity of the renormalization group approach to critical phenomena.