New critical phenomena in 2d quantum gravity

TL;DR

This paper investigates the phase transitions of Potts models with high q-values on dynamical triangulated lattices, revealing continuous transitions and structural changes in the underlying surfaces, contrasting with regular lattice behavior.

Contribution

It demonstrates that high-q Potts models on dynamical lattices exhibit continuous phase transitions and structural changes, unlike the first-order transitions on regular lattices.

Findings

q=10 shows second-order transition

q=200 shows third-order transition

Surface structure shifts from tree-like to fractal below critical temperature

Abstract

We study $q=10$ and $q=200$ state Potts models on dynamical triangulated lattices and demonstrate that these models exhibit continuous phase transitions, contrary to the first order transition present on regular lattices. For $q=10$ the transition seems to be of 2nd order, while it seems to be of 3rd order for $q=200$. For $q=200$ the phase transition also induces a transition between typical fractal structures of the piecewise linear surfaces corresponding to the triangulations. The typical surface changes from having a tree-like structure to a fractal structure characterizing pure gravity when the temperature drops below the critical temperature. An investigation of the alignment of spin clusters shows that they are strongly correlated to the underlying fractal structure of the triangulated surfaces.