Universal scaling and the essential singularity at the Ising first-order transition

The Ising model is perhaps the most-studied problem in physics. Near its continuous phase transition the model's thermodynamic quantities diverge or vanish with power laws and logarithms. The renormalization group connects the exponents in these functions to those of an {\sc rg} fixed point because, as an analytic transformation, it preserves all nonanalytic behavior. These power laws and logarithms are not the only nonanalytic feature near the critical point, however---as one approaches the line of first order transitions as $H\to0$ for $T