Numerical Simulation of Random Paths With a Curvature-Dependent Action

Abstract

We study an ensemble of closed random paths, embedded in R 3 , with a curvature dependent action. Previous analytical results indicate that there is no crumpling transition for any finite value of the curvature coupling. Nevertheless, in a high statistics numerical simulation, we observe two different regimes for the specific heat separated by a rather smooth structure. The analysis of this fact warns us about the difficulties in the interpretation of numerical results obtained in cases where theoretical results are absent and a high statistics simulation is unreachable. This may be the case of random surfaces.

Perturbative quantum field theory in the string-inspired formalism

“…Much less obvious is the converse question, which is whether a "sensible" worldline Lagrangian must always be induced by a spacetime Lagrangian, or whether worldline path integrals can perhaps be used to define physically relevant S-matrices which do not correspond to Lagrangian field theories. The use of an additional worldline curvature term [275,276,277] could be seen as a step in this direction.…”

Random paths with curvature

“…We have performed the first numerical analysis of a set of random paths with a curvature dependent action [10]. In addition to the intrinsic interest of this study, such a simulation can also be considered as a simple case to contrast the numerical work performed in the simulation of crystaline random surfaces and, in particular to compare with the analysis of the nature of the crumpling transition.…”