The Ising model with a boundary magnetic field on a random surface

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dc.creatorCarroll, Sean M.
dc.creatorOrtiz, Miguel E.
dc.creatorTaylor IV, Washington
dc.date1996-05-22
dc.date1996-05-23
dc.date.accessioned2026-07-07T11:14:49Z
dc.date.available2026-07-07T11:14:49Z
dc.descriptionThe bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field theory coupled to 2D quantum gravity, with a boundary term breaking conformal invariance. It is found that as h increases, the average magnetization of a bulk spin decreases, an effect that is explained in terms of fluctuations of the geometry. By introducing an $h$-dependent rescaling factor, the disk partition function and bulk magnetization can be expressed as functions of an effective boundary length and bulk area with no further dependence on h, except that the bulk magnetization is discontinuous and vanishes at h = 0. These results suggest that just as in flat space, the boundary field generates a renormalization group flow towards h = \infty. An exact analytic expression for the boundary magnetization as a function of $h$ is linear near h = 0, leading to a finite nonzero magnetic susceptibility at the critical temperature.
dc.description9 pages inc. 2 figures, revtex, cosmetic changes
dc.identifierhttps://arxiv.org/abs/hep-th/9605169
dc.identifierhttp://arxiv.org/abs/hep-th/9605169
dc.identifierPhys.Rev.Lett.77:3947-3950,1996
dc.identifierdoi:10.1103/PhysRevLett.77.3947
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/192204
dc.subjectHigh Energy Physics - Theory
dc.subjectCondensed Matter
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleThe Ising model with a boundary magnetic field on a random surface
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