Quantum Chromodynamics, Antiferromagnets and XY Models from a Unified Point of View

TL;DR

This paper demonstrates that antiferromagnets, quantum XY magnets, and quantum chromodynamics share a common effective Lagrangian structure, revealing universal features in their low-temperature behavior despite vastly different energy scales.

Contribution

It establishes a unified effective field theory framework for these systems, highlighting their similar low-temperature expansions and the emergence of logarithmic terms in nonabelian cases.

Findings

Logarithmic $T^8 \ln T$ terms appear at three-loop order for nonabelian systems.

For $N=2$, the series involves only powers of $T^2$.

The Goldstone boson interactions affect pressure, order parameter, and susceptibility in external fields.

Abstract

Antiferromagnets and quantum XY magnets in three space dimensions are described by an effective Lagrangian that exhibits the same structure as the effective Lagrangian of quantum chromodynamics with two light flavors. These systems all share a spontaneously broken internal symmetry O($N$) $\to$ O($N$-1). Although the respective scales differ by many orders of magnitude, the general structure of the low-temperature expansion of the partition function is the same. In the nonabelian case, logarithmic terms of the form $T^8 \ln T$ emerge at three-loop order, while for $N$=2 the series only involves powers of $T^2$. The manifestation of the Goldstone boson interaction in the pressure, order parameter, and susceptibility is explored in presence of an external field.