Liquid helium becomes a superfluid and flows with zero viscosity at low temperatures. Superfluidity is manifested by a failure to rotate, as its mass is decoupled from the rotation of the containing cell. Supersolid helium should show similar behaviour; apparent rotational inertia decreases when the solid helium is set into torsional oscillation below 200 mK (refs 1,2) Unlike a typical superfluid, the non-classical rotational inertia fraction (NCRIF) has been found to be partially hysteretic 8 . The low-temperature (T <∼ 20 mK) value of NCRIF for a sample was smaller when cooled down in a high-velocity field (HVF), versus that obtained at low speeds. On reducing the velocity at the lowest temperature, the NCRIF recovered the unsuppressed value. However, subsequent increases in the velocity did not result in any suppression of the NCRIF up to at least 800 µm s −1 . This hysteresis was observed only below about 40 mK. Slow warming and cooling cycles (all below 65 mK) following the above type of velocity sweeps have revealed that the NCRIF can be multivalued at the lowest temperatures 9 . The two research groups involved have described these findings in terms of the pinning of low-temperature excitations (such as dislocations and/or vortices) in solid 4 He. Here we examine the phenomena systematically by measuring the dynamic response of a torsional oscillator containing a bulk 4 He sample at a pressure of 40 bar. The sample was grown using the blocked capillary method. The torsional oscillator has an open volume of 1.92 cm 3 in a cylindrical form, with a 13 mm diameter and a height of 14.5 mm. The surface-area to volume (S/V ) ratio is 4.46 cm −1 . The empty cell has a resonant period of 1.328 ms and a mechanical quality factor of 2×10 6 at 4.2 K. Two procedures were used to reach a fixed temperature and rim velocity, both of which represent a different history. The first is a typical method from previous studies. After setting the driving voltage at 500 mK, the torsional oscillator was cooled to the base temperature of 23 mK. After equilibration at the lowest temperature, a slow warming scan was carried out. We will refer to this cooling procedure and the corresponding NCRIF as HVF cooling and HVF NCRIF, respectively. As the rim velocity v R of the torsional oscillator is temperature dependent for a constant driving voltage, we consistently denote each data set by the value of v R recorded at 23 mK.The second procedure was as follows. At 500 mK, the driving voltage was set to a low value such that v R at 23 mK is less than

Using Monte Carlo simulations we study bond percolation on a random two-dimensional lattice. We find that although the critical exponents appear to be the same as for percolation on a regular lattice, the ratio of critical amplitudes, which is also supposed to be universal, is diA'erent.