Related papers: Renormalization Group Approach to Matrix Models in…
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
The renormalization group approach is studied for large $N$ models. The approach of Br\'ezin and Zinn-Justin is explained and examined for matrix models. The validity of the approach is clarified by using the vector model as a similar and…
We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the…
A Yang-Mills type two matrix model with mass terms is studied by use of a matrix renormalization group approach proposed by Brezin and Zinn-Justin. The renormalization group method indicates that the model exhibits a critical behavior…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
We develop a new renormalization group approach to the large-N limit of matrix models. It has been proposed that a procedure, in which a matrix model of size (N-1) \times (N-1) is obtained by integrating out one row and column of an N…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
We develop a method to obtain the large N renormalization group flows for matrix models of 2 dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one matrix models. We show…
We summarize our recent results on the large N renormalization group (RG) approach to matrix models for discretized two-dimensional quantum gravity. We derive exact RG equations by solving the reparametrization identities, which reduce…
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling…
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group…
We revisit Fradkin and Raby's real-space renormalization-group method to study the quantum Z_2 gauge theory defined on links forming a two-dimensional square lattice. Following an old suggestion of theirs, a systematic perturbation…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
We compute the critical exponents of $d = 1$ string theory to leading order, using the renormalization group approach recently suggested by Br\'{e}zin and Zinn-Justin.
A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size…
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. The idea is to update link flips on the block lattice in response to link flips on the original lattice.…
A renormalization-group scheme is developed for the 3-dimensional O($2N$)-symmetric Ginzburg-Landau-Wilson model, which is consistent with the use of a 1/N expansion as a systematic method of approximation. It is motivated by an application…