We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $sigma$ and for large sizes. We observe that the resu
lts close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.
The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying only confo
rmal invariance, the so called minimal conformal field theories (CFTs). We consider interfaces in Z(N) spin models at their self-dual critical point for N=4 and N=5. These lattice models are described in the continuum limit by non-minimal CFTs where the role of a Z_N symmetry, in addition to the conformal one, should be taken into account. We provide numerical results on the fractal dimension of the interfaces which are SLE candidates for non-minimal CFTs. Our results are in excellent agreement with some recent theoretical predictions.
