Analytic verification of the droplet picture in the two-dimensional Ising model

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dc.creatorRutkevich, S. B.
dc.date2000-08-02
dc.date2000-09-07
dc.date.accessioned2026-07-07T02:38:23Z
dc.date.available2026-07-07T02:38:23Z
dc.descriptionIt 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}.
dc.description20 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
dc.identifierhttps://arxiv.org/abs/cond-mat/0008033
dc.identifierhttp://arxiv.org/abs/cond-mat/0008033
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/16649
dc.subjectCondensed Matter
dc.titleAnalytic verification of the droplet picture in the two-dimensional Ising model
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