Abstract
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 Cn in the power series expansions of the magnetizationm in the form m(H)=1 + ∑Cn(H-H 0 )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=Hsp(Ti < 0.
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Privman, V., Schulman, L.S. Analytic continuation at first-order phase transitions. J Stat Phys 29, 205–229 (1982). https://doi.org/10.1007/BF01020783
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DOI: https://doi.org/10.1007/BF01020783