Figure 5
From: The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model

Exact numerical results in 2D for t2/t = 0, ±0.025.
Note that the scaling of ωE maps the NNN calculations back to the original. This is in agreement with our approximate perturbation theory results, though perhaps serendipitously since the approximate perturbation theory was not very close to the exact numerical perturbation theory.