Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction

TL;DR

This paper uses effective Lagrangians to explicitly evaluate the thermodynamic properties of ferromagnetic spin chains at low temperatures, revealing how spin-wave interactions manifest and affect physical quantities.

Contribution

It provides the first detailed three-loop calculation showing the impact of spin-wave interactions in ferromagnetic spin chains using effective field theory methods.

Findings

Spin-wave interaction appears at order T^{5/2} in free energy.

The interaction is repulsive, as indicated by the positive coefficient.

The method surpasses traditional spin-wave theory in complexity and detail.

Abstract

The thermodynamic properties of ferromagnetic spin chains have been the subject of many publications. Still, the problem of how the spin-wave interaction manifest itself in these low-temperature series has been neglected. Using the method of effective Lagrangians, we explicitly evaluate the partition function of ferromagnetic spin chains at low temperatures and in the presence of a magnetic field up to three loops in the perturbative expansion where the spin-wave interaction sets in. We discuss in detail the renormalization and numerical evaluation of a particular three-loop graph and derive the low-temperature series for the free energy density, energy density, heat capacity, entropy density, as well as the magnetization and the susceptibility. In the low-temperature expansion for the free energy density, the spin-wave interaction starts manifesting itself at order $T^{5/2}$. In the pressure, the coefficient of the $T^{5/2}$-term is positive, indicating that the spin-wave interaction is repulsive. While it is straightforward to go up to three-loop order in the effective loop expansion, the analogous calculation on the basis of conventional condensed matter methods, such as spin-wave theory, appears to be beyond reach.