Finite-size scaling in the complex temperature plane applied to the three-dimensional Ising model

We extend the finite-size scaling theory into the complex temperature plane and present an alternative scenario for the second-order phase transition where the second-order derivatives of the partition function diverge at the transition point with the same exponent but different (discontinuous) amplitudes ${\mathit{A}}_{\pm }$. The complex scaling partition function ${\mathit{Z}}_{\mathit{s}}$ for the d=3 Ising model on a simple-cubic lattice is calculated using microcanonical Monte Carlo technique and is used to verify the scenario. The method of complex ${\mathit{Z}}_{\mathit{s}}$ can be used as an alternative to the series method for the study of the second-order phase transition.