Complex zeros of the 2d Ising model on dynamical random lattices

Details Complex zeros of the 2d Ising model on dynamical random lattices Complex zeros of the 2d Ising model on dynamical random lattices

1997-08-20

arxiv.org/abs/hep-lat/9708014v1

Nucl.Phys.Proc.Suppl. 63 (1998) 751-753

Physics

High Energy Physics

High Energy Physics - Lattice

3 pages, 8 figures, latex2e, uses espcrc2.sty. Contribution to Lattice '97, Edinburgh, July 1997, to appear on Nucl. Phys. B (

Scientific paper

10.1016/S0920-5632(97)00893-1

We study the zeros in the complex plane of the partition function for the Ising model coupled to $2d$ quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two matrix model and by Monte Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional patterns in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of singularities near the critical point.

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