Five-loop \sqrt\epsilon-expansions for random Ising model and marginal spin dimensionality for cubic systems

TL;DR

This paper computes five-loop -expansions for critical exponents in the disordered Ising model and estimates the marginal spin dimensionality for cubic systems using advanced resummation techniques.

Contribution

It provides high-order -expansions for critical exponents and a new estimate of the marginal spin dimensionality for cubic models, enhancing understanding of disordered magnetic systems.

Findings

Five-loop -expansions with irregular coefficients

Estimated marginal spin dimensionality n_c  2.855

Resummation improves critical exponent predictions

Abstract

The \sqrt\epsilon-expansions for critical exponents of the weakly-disordered Ising model are calculated up to the five-loop order and found to possess coefficients with irregular signs and values. The estimate n_c = 2.855 for the marginal spin dimensionality of the cubic model is obtained by the Pade-Borel resummation of corresponding five-loop \epsilon-expansion.