Determine the correlation-length exponent in three-dimensional disordered Weyl semimetals

Determine the correlation-length exponent for the disorder-driven Weyl semimetal-to-metal quantum phase transition in three spatial dimensions, including whether higher-order terms in the ε_m expansion resolve the discrepancy between the numerically observed value near one and the leading-order prediction.

Background

The paper identifies four spatial dimensions as the upper critical dimension of the disorder-driven Weyl semimetal-to-metal transition and finds a mean-field correlation-length exponent ν≈0.5 for dimensions d≥4. In d=3, however, the numerical estimate is ν≈1, while the leading-order ε_m expansion predicts ν=1, and the authors note that the issue remains unresolved in the broader theoretical description.

The authors specifically identify the unknown higher-order corrections to ν in the ε_m expansion as a possible route to settling the unresolved behavior in three dimensions. This problem concerns the systematic determination of those corrections and their ability to account for the observed critical exponent.