Universality in two-dimensional Ising models

Abstract

We have used finite-size scaling and transfer matrix techniques to calculate accurately the critical exponents of three two-dimensional Ising-like models for which no exact solution is available: two spin- 1 2 models with crossing bonds, and a spin-1 model. The results for the temperature and magnetic exponents are very close to the exact results for exactly solvable models which are assumed to be in the same universality class. Differences are between 10 -5 and a few times 10 -4, and within the apparent numerical uncertainties. We also present an estimate of the critical point of the spin-1 model, and some preliminary results concerning universal properties of critical amplitudes.