Phase Transition in Dually Weighted Colored Tensor Models

TL;DR

This paper introduces a new class of colored tensor models with weighted faces, enabling the study of higher-dimensional triangulations with curvature, and analytically demonstrates a phase transition in a specific model.

Contribution

The authors develop a novel weighted tensor model framework and analytically solve the leading order, revealing a phase transition in the continuum limit.

Findings

Analytical solution of leading order in 1/N for general models

Identification of a third-order phase transition in a specific model

Introduction of face-weighted tensor models for higher-dimensional triangulations

Abstract

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models with a modified propagator which allows us to associate weight factors to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation, where curvature is concentrated. They correspond to dynamical triangulations in three and higher dimensions with generalized amplitudes. We solve analytically the leading order in 1/N of the most general model in arbitrary dimensions. We then show that a particular model, corresponding to dynamical triangulations with a non-trivial measure factor, undergoes a third-order phase transition in the continuum characterized by a jump in the susceptibility exponent.