General Theory of Spin-Wave Interactions
1956/06/01 by Freeman J. Dyson · 1,634 citations
Physics and Astronomy · #Bethe lattice #Condensed matter physics #Curie temperature #Ferromagnetism #Ising model #Isotropy #Lattice (music) #Magnetic properties of thin films #Physics #Quantum and electron transport phenomena #Quantum mechanics #Spin (aerodynamics) #Spin wave #Spins #Theoretical and Computational Physics
paper · doi:10.1103/physrev.102.1217
published in Physical Review 102(5), 1217-1230 (American Institute of Physics)
openalex publication_date 1956/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract
An ideal model of a ferromagnet is studied, consisting of a lattice of identical spins with cubic symmetry and with isotropic exchange coupling between nearest neighbors. The aim is to obtain a complete description of the thermodynamic properties of the system at low temperatures, far below the Curie point. In this temperature region the natural description of the states of the system is in terms of Bloch spin waves. The nonorthogonality of spin-wave states raises basic difficulties which are examined and overcome.The following new results are obtained: a practical method for calculating thermodynamic quantities in terms of a nonorthogonal set of basic states; a proof that in 3 dimensions there do not exist states (shown by Bethe to exist in a one-dimensional chain of spins) in which two spins are bound together into a stable complex and travel together through the lattice; a calculation of the scattering cross section of two spin waves, giving a mean free path for spin-spin collisions proportional to T^\ensuremath-(7)/(2) at low temperatures; and an exact formula for the free energy of the system, showing explicitly the effects of spin-wave interactions.Quantitative results based on this theory will be published in a second paper.
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