Wilsonian Approximated Renormalization Group for Matrix and Vector Models in 2<d<4

Abstract

Wilson's approximation scheme of RG recursion formula dropping momentum dependence of the propagators is applied to large-$N$ vector and matrix models in dimensions $2<d<4$ by making use of their exact solutions in zero dimension. In spite of apparent dependence of critical exponents upon the dilatational parameter $\rho$ involved by the approximation, the exact exponents are reproduced for vector models in the limit $\rho \to 0$. Application to matrix models is then reexamined after the same fashion. It predicts critical exponents $\nu =2/d$ and $\eta =2-d/2$ for the $\tr Φ^4$ matrix model.

11 pages, 2 PostScript figures, LaTeX + epsf.tex. Remarks on subleading exponents supplemented. To be published in Phys.Lett.B

References in corpus (4)

• 2D Gravity and Random Matrices
• Renormalization Group Approach to Matrix Models
• Light-Cone Quantization of the c=2 Matrix Model
• On the Large N Limit of 3D and 4D Hermitian Matrix Models

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