Essential Singularities in Universal Scaling Functions at the Ising Coexistence Line

Jaron Kent-Dobias, James P. Sethna

Published 2017-07-12Version 1

Renormalization group ideas and results from critical droplet theory are used to construct a scaling ansatz for the imaginary component of the free energy of an Ising model in its metastable state close to the critical point. The analytic properties of the free energy are used to determine scaling functions for the free energy in the vicinity of the critical point and the abrupt transition line. These functions have essential singularities at zero field. Analogous forms for the magnetization and susceptibility in two dimensions are fit to numeric data and show good agreement.