On Spin and Matrix Models in the Complex Plane

Details On Spin and Matrix Models in the Complex Plane On Spin and Matrix Models in the Complex Plane

1993-07-22

arxiv.org/abs/hep-lat/9307016v1

Nucl.Phys. B410 (1993) 494-520

Physics

High Energy Physics

High Energy Physics - Lattice

25 pages with 5 postscript figures included. LaTeX file with style file crnart11.sty included. CERN--TH-6956/93, FSU-SCRI-93-8

Scientific paper

10.1016/0550-3213(93)90526-U

We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of 2-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-$N$ partition function zeros in the complex plane.

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