Analytic properties of thermodynamic functions at first-order phase transitions

Develops a method of analytic continuation at first-order phase transitions and applies it to the d=2 Ising model in an external field. The method employs a function built of transfer matrix eigenvalues, which provides rapidly convergent approximations to the stable free energy f and its derivatives for all H>or=0. Recent series analysis results on the existence of an essential singularity at H=0 are confirmed. There is also an indication of a spinodal line, and H sp (T)<O is estimated in the range O<T