Testing perturbative results with non-perturbative methods for the Hierarchical model

TL;DR

This paper develops non-perturbative techniques to precisely compute renormalized quantities in Dyson's Hierarchical Model, achieving high-precision critical exponents and universal ratios, and compares these with perturbative predictions.

Contribution

It introduces non-perturbative methods for accurate calculations in Dyson's Hierarchical Model, enhancing precision in critical exponents and universal ratios.

Findings

Critical exponent gamma calculated with 12 significant digits in high-temperature phase.

Critical exponent gamma calculated with 4 significant digits in low-temperature phase.

Universal ratios of amplitudes determined with high accuracy.

Abstract

We present non-perturbative methods to calculate accurately the renormalized quantities for Dyson's Hierarchical Model. We apply this method and calculate the critical exponent gamma with 12 and 4 significant digits in the high and low temperature phases, respectively. We report accurate values for universal ratios of amplitudes and preliminary results concerning the comparison with perturbative results.