  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.
