Droplet Theory of Low-Dimensional Ising Models

A droplet theory of Ising systems is constructed, valid near space dimension $d=1\mathrm{}$, and based on a model incorporating only the configurational energy of surface tension. The droplet distribution function is calculated explicitly, with use of renormalization-group methods to control the droplet-shape fluctuation effects essential to its scaling form. Universal quantities are calculated; those (e.g., $\beta$) which reflect the droplet concentration have an essential singularity in $\epsilon =d-1\mathrm{}$.