Scaling limit of the energy variable for the two-dimensional Ising ferromagnet
The critical point limit law (scaling limit) of the suitably renormalized energy variable is explicitly calculated for the two-dimensional nearest- neighbour Ising cylinder with free edges. It is shown that the renormalization factor has to behave as (2M 2N ln N)\({}^{1/2}\), where 2M denotes the number of rows and 2N the number of columns. By first taking the limit \(M\to \infty\) and then \(N\to \infty\), the limit law is proved to be Gaussian.
two-dimensional nearest-neighbour Ising cylinder
scientific article; zbMATH DE number 3913421