Essential singularities in dilute magnets

Abstract

Harris argued in favor of an essential singularity at zero magnetic field in the equation of state for randomly dilute low-temperature ferromagnets. His assumptions and conclusions are reexamined and criticized with the help of earlier Monte Carlo data on the number $W_n$ of clusters with $n$ spins each. These data suggest for large clusters $log{W}_n\propto - n$ on the paramagnetic side, whereas $log{W}_n\propto - n^{0.4}$ on the ferromagnetic side. More Monte Carlo work is suggested, if $n\sim 100$, for square site percolation near $p=0.40\mathrm{}$ or square bond percolation near $p=0.35\mathrm{}$.