Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-05-22
Phys.Rev.Lett.77:3947-3950,1996
Physics
High Energy Physics
High Energy Physics - Theory
9 pages inc. 2 figures, revtex, cosmetic changes
Scientific paper
10.1103/PhysRevLett.77.3947
The 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.
Carroll Sean M.
IV Washington Taylor
Ortiz Miguel E.
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