Scaling and universality in the two-dimensional Ising model with a magnetic field

The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter’s variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.

Figure 1

The scaling function $\Phi \left(\eta \right)$ in the three regions, separated by the dashed lines at $\eta \simeq \pm 2.43$, can be approximated with relative precision ${10}^{-4}$ by the series (9), (10), and (8). The required coefficients to achieve this precision given in Table .