Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity

Details Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity

1997-05-02

arxiv.org/abs/hep-lat/9705004v2

Mod.Phys.Lett. A12 (1997) 1605-1628

Physics

High Energy Physics

High Energy Physics - Lattice

22 pages, LaTeX2e, 10 figures, added discussion on antiferromagnetic transition and references

Scientific paper

10.1142/S0217732397001643

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 real temperature, and for complex temperature and real magnetic field, respectively. 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 curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.

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