Universality of Second-Order Phase Transitions: The Scale Factor for the Correlation Length

Abstract

A universality hypothesis relates the amplitude of the singular parts of the coherence length and the specific heat (or surface tension). For the spin-½ Ising model it is exact in two dimensions and numerically accurate to within 1% in three. It is consistent with measurements on the "Ising-like" systems C${\mathrm{O}}_2$, Xe, and $\beta$-brass and the "Heisenberg-like" systems RbMn${\mathrm{F}}_3$ and EuS to within experimental uncertainties (∼ 20%). It provides a sensitive and experimentally convenient indicator of symmetry ("universality") class.