Correction exponents in the chiral Heisenberg model at $1/N^2$: singular contributions and operator mixing

TL;DR

This paper computes correction exponents in the chiral Heisenberg model using a $1/N^2$ expansion, revealing divergence near three dimensions due to operator mixing, and proposes a resummation method validated by direct 3D calculations.

Contribution

It provides the first $1/N^2$ order calculation of correction exponents in the chiral Heisenberg model and introduces a resummation technique accounting for operator mixing effects.

Findings

Correction exponents diverge as $d o 3$.

Resummation modifies exponents at leading order.

Agreement with direct 3D calculations confirms validity.

Abstract

We calculate the correction exponents in the chiral Heisenberg model in the $1/N$ expansion. These exponents are related to the slopes of $\beta$ functions at the phase transition point. We present the results at order $1/N^2$ and check that they agree with the results of the $\epsilon$ expansion near $d = 4$. We find that one of the correction exponents diverges as $d \to 3$. We argue that the appearance of the pole is a rather general phenomenon and is associated with operator mixing involving the system of four-fermion operators. After analyzing the operator mixing structure, we propose a resummation procedure which modifies the exponents already at leading order. We also perform calculations directly in the three-dimensional model and find complete agreement with the resummed exponents.