Power-law singularities and critical exponents in n-vector models

TL;DR

This paper compares theoretical approaches to power-law singularities and critical exponents in n-vector models, providing non-perturbative proofs and analyzing experimental and simulation data to support the GFD theory over perturbative RG.

Contribution

It introduces the GFD theory as a viable alternative to perturbative RG for explaining critical phenomena in n-vector models, supported by non-perturbative proofs and data analysis.

Findings

GFD theory predictions align well with experimental data near lambda-transition in liquid helium.

Monte Carlo simulations of Goldstone mode singularities support GFD theory.

Non-perturbative proof shows corrections to scaling favor GFD over perturbative RG.

Abstract

Power-law singularities and critical exponents in n-vector models are considered from different theoretical points of view. It includes a theoretical approach called the GFD (grouping of Feynman diagrams) theory, as well as the perturbative renormalization group (RG) treatment. A non-perturbative proof concerning corrections to scaling in the two-point correlation function of the phi^4 model is provided, showing that predictions of the GFD theory rather than those of the perturbative RG theory can be correct. Critical exponents determined from highly accurate experimental data very close to the lambda-transition point in liquid helium, as well as the Goldstone mode singularities in n-vector spin models, evaluated from Monte Carlo simulation results, are discussed with an aim to test the theoretical predictions. Our analysis shows that in both cases the data can be well interpreted within the GFD theory.