2000/08/02 by S. B. Rutkevich, Rutkevich, S. B.
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/0008033
20 pages, LaTeX2e, 3 PNG figures, Poster presented at the ``XIII International Congress on Mathematical Physics'', July 17-22, 2000, London, UK, revised version, appendix and references added
arxiv created 2000/09/07 · arxiv updated 2009/11/30
It is widely accepted that the free energy F(H) of the two-dimensional Ising model in the ferromagnetic phase T<Tc has an essential branch cut singularity at the origin H=0. The phenomenological droplet theory predicts that near the cut drawn along the negative real axis H<0, the imaginary part of the free energy per lattice site has the form Im F[exp (± iπ|H|)] = ± B |H| exp (-A/|H|) for small |H|. We verify this prediction in analytical perturbative transfer matrix calculations for the square lattice Ising model for all temperatures 0<T<Tc and arbitrary anisotropy ratio J1/J2. We obtain an expression for the constant A which coincides exactly with the prediction of the droplet theory. For the amplitude B we obtain B =πM/18, where M is the equilibrium spontaneous magnetization. In addition we find discrete-lattice corrections to the above mentioned phenomenological formula for ImF, which oscillate in H-1.