Molecular dynamics simulation of tethered membranes in four and five dimensions

We have carried out extensive molecular dynamics simulations of self-avoiding tethered membranes embedded in four- and five-dimensional space. These calculations were performed for a wide range of effective hard-core diameters in order to determine whether or not a crumpling transition exists. We find, in agreement with previous work, that self-avoiding tethered membranes are always flat in d=4 and crumpled in d=5.