Phase Transition in Dually Weighted Colored Tensor Models

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.

17 pages, 4 figures; v2: two references added

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Cited by in corpus (45)

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• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• The Tensor Track, III
• Coarse graining methods for spin net and spin foam models
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Ten questions on Group Field Theory (and their tentative answers)
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• Invitation to Random Tensors
• Lattice Quantum Gravity and Asymptotic Safety
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Group field theories for all loop quantum gravity
• Path integral measure and triangulation independence in discrete gravity
• Melonic phase transition in group field theory
• Towards a double-scaling limit for tensor models: probing sub-dominant orders
• The Double Scaling Limit in Arbitrary Dimensions: A Toy Model
• Correlation functions of just renormalizable tensorial group field theory: The melonic approximation
• Two and four-loop $\beta$-functions of rank 4 renormalizable tensor field theories
• Boosting Wigner's nj-symbols
• Canonical tensor models with local time
• Euclidian 4d quantum gravity with a non-trivial measure term
• Uniqueness of canonical tensor model with local time
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry
• Coupling of hard dimers to dynamical lattices via random tensors
• A Renormalizable 4-Dimensional Tensor Field Theory
• Ward identity violation for melonic $T^4$-truncation
• The Complete Barrett-Crane Model and its Causal Structure
• Towards background independent quantum gravity with tensor models
• Infrared divergences in the EPRL-FK Spin Foam model
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• Ward-constrained melonic renormalization group flow
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• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• Renormalizable Models in Rank $d\ge 2$ Tensorial Group Field Theory
• Complex Path Integrals and the Space of Theories
• Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow
• $(D+1)$-Colored Graphs - a Review of Sundry Properties
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• Studying the EPRL spinfoam self-energy
• Landau Theory of Causal Dynamical Triangulations