We study the Parisi overlap probability density $P_L\mathrm{}\left(q\right)\mathrm{}$ for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point, $P_L\mathrm{}\left(q\right)\mathrm{}$ is peaked around $q=0\mathrm{}$ in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multioverlap MC algorithm. Below the critical temperature, interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.

• Received 17 May 2002

DOI:https://doi.org/10.1103/PhysRevE.66.046122