Analytic continuation at first-order phase transitions

We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH 0. This new function is used for numerical calculation of the coefficients C_n in the power series expansions of the magnetizationm in the form m(H)=1 + C_n(H-H₀)ⁿ for various H₀ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=H_sp(Ti < 0.