What question did this study set out to answer?

This research aims to calculate correction exponents in the chiral Heisenberg model using the 1/N expansion.

June 17, 2026Open Access

Correction exponents in the chiral Heisenberg model at 1/N²: singular contributions and operator mixing

Key Points

This research aims to calculate correction exponents in the chiral Heisenberg model using the 1/N expansion.
Calculating correction exponents at order 1/N2
Comparing with epsilon expansion results near d=4
Analyzing operator mixing involving four-fermion operators
One correction exponent diverges as d approaches 3
Findings agree with epsilon expansion results
Direct calculations in the three-dimensional model confirm resummed exponents

Abstract

Abstract We calculate the correction exponents in the chiral Heisenberg model in the 1/ N expansion. These exponents are related to the slopes of β functions at the phase transition point. We present the results at order 1/N² 1 / N 2 and check that they agree with the results of the ϵ expansion near d = 4 d = 4. We find that one of the correction exponents diverges as d 3 d → 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.

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