Analytic verification of the droplet picture in the twodimensional Ising model
Abstract
It is widely accepted that the free energy F(H) of the twodimensional 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 i\pi 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 =\pi M/18, where M is the equilibrium spontaneous magnetization. In addition we find discretelattice corrections to the above mentioned phenomenological formula for ImF, which oscillate in H^{1}.
 Publication:

arXiv eprints
 Pub Date:
 August 2000
 arXiv:
 arXiv:condmat/0008033
 Bibcode:
 2000cond.mat..8033R
 Keywords:

 Condensed Matter
 EPrint:
 20 pages, LaTeX2e, 3 PNG figures, Poster presented at the ``XIII International Congress on Mathematical Physics'', July 1722, 2000, London, UK, revised version, appendix and references added