On the Transition from Crystalline to Dynamically Triangulated Surfaces

TL;DR

This paper explores methods to interpolate between crystalline and dynamically triangulated surface models, proposing an alternative approach based on Alexander moves, and analyzing two simplified models with different phase transition behaviors.

Contribution

It introduces a new interpolation method using Alexander moves and compares two simplified models, one exhibiting a phase transition and the other not.

Findings

One model exhibits a phase transition.

The other model does not exhibit a phase transition.

Proposes an alternative to deviation-based actions.

Abstract

We consider methods of interpolating between the crystalline and dynamically triangulated random surface models. We argue that actions based on the deviation from six of the coordination number at a site are inadequate and propose an alternative based on Alexander moves. Two simplified models, one of which has a phase transition and the other of which does not, are discussed.