Geometric expansion of the log-partition function of the anisotropic Heisenberg model

Daniel Gandolfo (1, 2) , Suren Poghosyan (3) , Jean Ruiz (2, 1)

1 CPT - E5 Physique statistique et systèmes complexes
2 CPT - Centre de Physique Théorique - UMR 7332
3 Institute of Mathematics, Armenian National Academy of Science

We study the asymptotic expansion of the log-partition function of the anisotropic Heisenberg model in a bounded domain as this domain is dilated to infinity. Using the Ginibre's representation of the anisotropic Heisenberg model as a gas of interacting trajectories of a compound Poisson process we find all the non-decreasing terms of this expansion. They are given explicitly in terms of functional integrals. As the main technical tool we use the cluster expansion method.

Domaines: Physique mathématique [math-ph]

Daniel Gandolfo, Suren Poghosyan, Jean Ruiz. Geometric expansion of the log-partition function of the anisotropic Heisenberg model. Journal of Mathematical Physics, 2015, 56 (9), pp.093302 ⟨10.1063/1.4931478⟩. ⟨hal-01262153⟩