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 in such a way that βS stays constant, we rigorously show that the free energy per unit volume converges to the one suggested by spin wave theory. The proof 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 remainder.

The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin

Correggi, Michele
;
Giuliani, A.
2012

Abstract

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 in such a way that βS stays constant, we rigorously show that the free energy per unit volume converges to the one suggested by spin wave theory. The proof 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 remainder.
2012
Settore MAT/07 - Fisica Matematica
Ferromagnetic Heisenberg model; Magnons; Spin waves; Statistical and Nonlinear Physics; Mathematical Physics
   Collective phenomena in quantum and classical many body systems
   COMBOS
   European Commission
   SEVENTH FRAMEWORK PROGRAMME
   239694
File in questo prodotto:
File Dimensione Formato  
1207.4050v1.pdf

accesso aperto

Tipologia: Submitted version (pre-print)
Licenza: Solo Lettura
Dimensione 198.42 kB
Formato Adobe PDF
198.42 kB Adobe PDF
s10955-012-0589-4.pdf

accesso aperto

Tipologia: Published version
Licenza: Creative Commons
Dimensione 550.54 kB
Formato Adobe PDF
550.54 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79635
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
  • OpenAlex ND
social impact