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

Abstract

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.

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

References in corpus (2)

• Quantum geometry of 2d gravity coupled to unitary matter
• Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity

Cited by in corpus (8)

• Thin Fisher Zeroes
• Fat Fisher Zeroes
• The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings
• Yang-Lee Zeros of the Ising model on Random Graphs of Non Planar Topology
• The Yang Lee Edge Singularity on Feynman Diagrams
• Kertesz on Fat Graphs?
• Yang-Lee Zeros of the Two- and Three-State Potts Model Defined on ${\varphi }^3$ Feynman Diagrams
• Fat and Thin Fisher Zeroes