Pseudo-epsilon expansion and the two-dimensional Ising model

TL;DR

This paper develops pseudo-epsilon expansions for key parameters of the two-dimensional Ising model using five-loop renormalization-group data, enabling accurate numerical estimates without complex resummation.

Contribution

It introduces pseudo-epsilon expansions for the 2D Ising model's fixed point, exponents, and couplings, simplifying numerical estimation procedures.

Findings

Higher-order terms in expansions are very small, allowing simple Pade approximants to yield accurate estimates.

Pseudo-epsilon expansions exhibit remarkable properties that facilitate straightforward numerical analysis.

The method provides an alternative to Borel resummation for critical parameter estimation.

Abstract

Starting from the five-loop renormalization-group expansions for the two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson fixed point coordinate g*, critical exponents, and the sextic effective coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse susceptibility exponent \gamma, and g_6 are found to possess a remarkable property - higher-order terms in these expansions turn out to be so small that accurate enough numerical estimates can be obtained using simple Pade approximants, i. e. without addressing resummation procedures based upon the Borel transformation.