Dimer model: Full asymptotic expansion of the partition function

We give a complete rigorous proof of the full asymptotic expansion of the partition function of the dimer model on a square lattice on a torus for general weights zh, zv of the dimer model and arbitrary dimensions of the lattice m, n. We assume m is even and we show that the asymptotic expansion dep...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical physics 2018-09, Vol.59 (9)
Hauptverfasser: Bleher, Pavel, Elwood, Brad, Petrović, Dražen
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We give a complete rigorous proof of the full asymptotic expansion of the partition function of the dimer model on a square lattice on a torus for general weights zh, zv of the dimer model and arbitrary dimensions of the lattice m, n. We assume m is even and we show that the asymptotic expansion depends on the parity of n. We review and extend the results of Ivashkevich et al. [J. Phys. A: Math. Gen. 35, 5543 (2002)] on the full asymptotic expansion of the partition function of the dimer model, and we give a rigorous estimate of the error term in the asymptotic expansion of the partition function.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5035271