The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin
FM 7-12, arxiv:1207.4050
Authors M. Correggi, A. Giuliani
We consider the spin-S ferromagnetic Heisenberg model in three
dimensions, in the absence of
an external field. Spin wave theory suggests that in a suitable
temperature regime the system
behaves effectively as a system of non-interacting bosons (magnons).
We prove this fact at the level of the specific free energy: if
S→∞ and the inverse temperature β→0
a way that
β⋅ S stays constant, we rigorously show that the free energy per
converges to the one suggested by spin wave theory.
is based on the localization of the system in small boxes and on upper and
lower bounds on the
local free energy, and it also provides explicit error bounds on the