CRUMPLING DYNAMICALLY TRIANGULATED RANDOM SURFACES IN HIGHER DIMENSIONS

Recent numerical simulations have revealed an unexpected second order crumpling transition for dynamically triangulated random surfaces embedded in three and four dimensions, raising the possibility of defining a continuum string theory at this point. In this paper we explore the behaviour of the transition in higher embedding dimensions (d=5, 6, 8, 10, 15, 20, 26) and find that the second order transition persists, in disagreement with analytical predictions using the 1 d expansion, which might be expected to be valid for large d. We discuss the discrepancy and also observe that the variation of the phase transition point with d rules out the possibility that the continuum theory is a hexatic membrane. © 1990.