Differences and analogies between quantum chromodynamics and ferromagnets

TL;DR

This paper compares the low-energy effective theories of quantum chromodynamics and ferromagnets, highlighting the application of effective Lagrangian methods to ferromagnetic systems across different dimensions.

Contribution

It systematically studies ferromagnets using effective Lagrangian techniques up to three-loop order, extending beyond previous condensed matter approaches.

Findings

Effective theory works well in one dimension for ferromagnets.

Three-loop calculations provide new insights into low-temperature properties.

The approach bridges concepts between particle physics and condensed matter.

Abstract

The low-energy physics of quantum chromodynamics (QCD) and ferromagnets is dominated by Goldstone bosons. While the effective theory of QCD - chiral perturbation theory - is well established in the particle physics community, the systematic studies of ferromagnetic systems within the effective Lagrangian framework are not well-known. We analyze the low-temperature properties of ferromagnets in one, two and three space dimensions up to three-loop order in the effective expansion, i.e., beyond the accuracy of any previous results obtained with conventional condensed matter methods. In particular, in the nonrelativistic domain, the effective method perfectly works in one space dimension.