Spontaneous Magnetization of an Ideal Ferromagnet: Beyond Dyson's Analysis

Abstract

Using the low-energy effective field theory for magnons, we systematically evaluate the partition function of the O(3) ferromagnet up to three loops. Dyson, in his pioneering microscopic analysis of the Heisenberg model, showed that the spin-wave interaction starts manifesting itself in the low-temperature expansion of the spontaneous magnetization of an ideal ferromagnet only at order $T^4$. Although several authors tried to go beyond Dyson's result, to the best of our knowledge, a fully systematic and rigorous investigation of higher order terms induced by the spin-wave interaction, has never been achieved. As we demonstrate in the present paper, it is straightforward to evaluate the partition function of an ideal ferromagnet beyond Dyson's analysis, using effective Lagrangian techniques. In particular, we show that the next-to-leading contribution to the spontaneous magnetization resulting from the spin-wave interaction already sets in at order $T^{9/2}$ -- in contrast to all claims that have appeared before in the literature. Remarkably, the corresponding coefficient is completely determined by the leading-order effective Lagrangian and is thus independent of the anisotropies of the cubic lattice. We also consider even higher-order corrections and thereby solve -- once and for all -- the question of how the spin-wave interaction in an ideal ferromagnet manifests itself in the spontaneous magnetization beyond the Dyson term.

References in corpus (11)

• Introduction to Effective Field Theory
• Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
• Effective Lagrangian and Topological Interactions in Supersolids
• Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet
• Very High Precision Determination of Low-Energy Parameters: The 2-d Heisenberg Quantum Antiferromagnet as a Test Case
• 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
• Goldstone bosons in presence of charge density
• Constraint Effective Potential of the Magnetization in the Quantum XY Model
• Magnetization and magnon excitation energies of the magnetic semiconductors EuTe and EuO on the basis of the renormalized spin wave theory

Cited by in corpus (17)

• Effective Lagrangians for quantum many-body systems
• Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets
• Magnon-driven chiral charge and spin pumping and electron-magnon scattering from time-dependent quantum transport combined with atomistic spin dynamics theory
• Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons
• Thermodynamics of Two-Dimensional Ideal Ferromagnets - Three-Loop Analysis
• Low-Temperature Properties of Ferromagnetic Spin Chains in a Magnetic Field
• Interaction Corrections to Spin-Wave Theory in the Large-S Limit of the Quantum Heisenberg Ferromagnet
• Magnon Energy Renormalization and Low-Temperature Thermodynamics of O(3) Heisenberg Ferromagnets
• Magnetic Catalysis in Antiferromagnetic Films
• Systematic Effective Field Theory Analysis of the D=2+1 Quantum XY Model at Low Temperatures
• Goldstone Boson Interaction in D=2+1 (Pseudo-)Lorentz-Invariant Systems with a Spontaneously Broken Internal Rotation Symmetry
• Thermodynamics of Ferromagnetic Spin Chains in a Magnetic Field: Impact of the Spin-Wave Interaction
• Validity of spin wave theory for the quantum Heisenberg model
• Two-loop free energy of three-dimensional antiferromagnets in external magnetic and staggered fields
• Thermodynamics of the $d$=3+1 Quantum XY Model
• Square-Lattice Antiferromagnet Subjected to a Magnetic Field Aligned with the Order Parameter
• Geometry of Classical Nambu-Goldstone Fields