Monomers and Dimers

Ole J. Heilmann; Elliott H. Lieb

doi:10.1103/PhysRevLett.24.1412

Monomers and Dimers

Ole J. Heilmann and Elliott H. Lieb

Phys. Rev. Lett. 24, 1412 – Published 22 June 1970

Abstract

We prove that the free energy of an arbitrary monomer-dimer system is analytic in the density and temperature for nonzero density, and hence that the system has no phase transition. This result can also be used to locate the $z = e^{2 β h}$ roots of the Heisenberg ferromagnet or antiferromagnet at high temperature.

Received 1 May 1970

DOI:https://doi.org/10.1103/PhysRevLett.24.1412

Authors & Affiliations

Ole J. Heilmann^*,†

Kemisk Laboratorium III, H. C. Orsted Institutet, University of Copenhagen, Denmark

Elliott H. Lieb^*

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

^*Work partially supported by National Science Foundation Grant No. GP-9414.
^†Work partially supported by Statens Naturvidenskabelige Forskningsråd Grant No. 511-208/69.