Higher order corrections for anisotropic bootstrap percolation

We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with (1, 2)-neighbourhood and threshold r = 3. The first order asymptotics for the critical probability were recently determined by the first and second authors. Here we determine the following sharp second and third order asymptotics: We note that the second and third order terms are so large that the first order asymptotics fail to approximate pc even for lattices of size well beyond 1010(1000)