Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction
arXiv:1306.0600 · doi:10.1016/j.physb.2014.02.047
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 . In the pressure, the coefficient of the -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.
24 pages, 3 figures
References in corpus (11)
- Ferromagnetic behaviour in the strongly interacting two-component Bose gas
- Thermodynamics of Heisenberg ferromagnets with arbitrary spin in a magnetic field
- Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet
- Thermodynamics of low dimensional spin-1/2 Heisenberg ferromagnets in an external magnetic field within Green function formalism
- Constraint Effective Potential of the Staggered Magnetization in an Antiferromagnet
- Homogeneous versus Spiral Phases of Hole-doped Antiferromagnets: A Systematic Effective Field Theory Investigation
- Systematic Low-Energy Effective Field Theory for Electron-Doped Antiferromagnets
- Constraint Effective Potential of the Magnetization in the Quantum XY Model
- Quantum versus classical behavior in the boundary susceptibility of the ferromagnetic Heisenberg chain
- Systematic Effective Field Theory Analysis of the D=2+1 Quantum XY Model at Low Temperatures
- Spiral phases and two-particle bound states from a systematic low-energy effective theory for magnons, electrons, and holes in an antiferromagnet