Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2001-05-02
Nucl.Phys. B614 (2001) 467-493
Physics
High Energy Physics
High Energy Physics - Lattice
32 pages, latex
Scientific paper
10.1016/S0550-3213(01)00405-9
We use Monte Carlo simulations to study a dynamically triangulated disk with Ising spins on the vertices and a boundary magnetic field. For the case of zero magnetic field we show that the model possesses three phases. For one of these the boundary length grows linearly with disk area, while the other two phases are characterized by a boundary whose size is on the order of the cut-off. A line of continuous magnetic transitions separates the two small boundary phases. We determine the critical exponents of the continuous magnetic phase transition and relate them to predictions from continuum 2-d quantum gravity. This line of continuous transitions appears to terminate on a line of discontinuous phase transitions dividing the small boundary phases from the large boundary phase. We examine the scaling of bulk magnetization and boundary magnetization as a function of boundary magnetic field in the vicinity of this tricritical point.
Bowick Mark
Catterall Simon
McGuire Scott
Warner Simeon
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