Analytic verification of the droplet picture in the two-dimensional Ising model
Abstract
Description
It is widely accepted that the free energy F(H) of the two-dimensional Ising model in the ferromagnetic phase T<T_c 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 (\pm iπ|H|)] = \pm 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<T_c and arbitrary anisotropy ratio J_1/J_2. 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}.
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
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