Cubic Ideal Ferromagnets at Low Temperature and Weak Magnetic Field

TL;DR

This paper develops a systematic effective field theory approach to analyze low-temperature properties of cubic ideal ferromagnets in weak magnetic fields, explicitly considering different lattice structures and providing formulas for thermodynamic quantities.

Contribution

It introduces a rigorous effective Lagrangian framework up to three loops for cubic ferromagnets, explicitly accounting for lattice structures and low-energy constants.

Findings

Derived low-temperature series for thermodynamic quantities

Analyzed spin-wave interactions and their effects

Provided formulas useful for consistency checks in other methods

Abstract

The low-temperature series for the free energy density, pressure, magnetization and susceptibility of cubic ideal ferromagnets in weak external magnetic fields are discussed within the effective Lagrangian framework up to three loops. The structure of the simple, body-centered, and face-centered cubic lattice is taken into account explicitly. The expansion involves integer and half-integer powers of the temperature. The corresponding coefficients depend on the magnetic field and on low-energy effective constants that can be expressed in terms of microscopic quantities. Our formulas may also serve as efficiency or consistency check for other techniques like Green's function methods, where spurious terms in the low-temperature expansion have appeared. We explore the sign and magnitude of the spin-wave interaction in the pressure, magnetization and susceptibility, and emphasize that our effective field theory approach is fully systematic and rigorous.