Monte Carlo study of the Ising ferromagnet on the site-diluted triangular lattice

In this paper we consider the Ising model on the triangular percolation lattice and analyze its geometrical interfaces and spin clusters. The (site) percolation lattice is tuned by the occupancy parameter p which is the probability that a site is magnetic. Some statistical observables are studied in terms of temperature (T) and p. We find two separate (second order) transition lines, namely magnetic and percolation transition lines. The finite size analysis shows that the magnetic transition line is a critical one with varying exponents, having its root in the fact that the line is composed of individual critical points, or that a cross-over occurs between two (UV and IR) fixed points. For the percolation transition line however the exponents seem to be identical. Schramm-Loewner evolution (SLE) is employed to address the problem of conformal invariance at the points on the magnetic transition line. We find that at p≃0.9 the model is described by κ≃4 whose corresponding central charge is maximum with respect to the others.