Universality in the crumpling transition

The addition of a term proportional to the extrinsic curvature in the action of surfaces embedded in d-dimensional space appears to induce a phase transition that separates smooth from crumpled surfaces - the crumpling transition. The nature of this phase transition is still object of much debate. We analyse this transition for d = 3 using a number of possible lattice translations of the continuum action in a fixed triangulation model using two different types of triangulations. In the light of previous conflicting numerical simulations, our main objective is to investigate to what extent universality ideas hold in random surfaces. We have performed long runs in relatively large systems paying careful attention to equilibration and binning. The simulations are notoriously difficult due to very large autocorrelation times, thus casting some doubts on the validity of the conclusions drawn in some previous work. Two choices for the action lead to transitions that, for the system sizes we use, are only marginally compatible with second-order transitions, while the third one exhibits a distinctive growth in the specific heat and we reproduce with great accuracy previous values for the critical exponents. On the other hand, there is clear universality with respect to the type of triangulation. We also find universality as far as the precise lattice transcription of the "area" action is concerned. © 1994.