The Ising model with a boundary magnetic field on a random surface
May, 19968 pages
Published in:
- Phys.Rev.Lett. 77 (1996) 3947-3950
e-Print:
- hep-th/9605169 [hep-th]
Report number:
- MIT-CTP-2536,
- IMPERIAL-TP-95-96-50,
- PUPT-1624
Citations per year
Abstract:
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 -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 is linear near h = 0, leading to a finite nonzero magnetic susceptibility at the critical temperature.- Ising model
- magnetic field
- partition function
- random surface
- statistical mechanics: continuum limit
- quantum gravity
- dimension: 2
- numerical calculations
References(21)
Figures(0)