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Chigak Itoi

Publications and source records attributed to Chigak Itoi.

32 records · Page 2Linked to original sources
arXiv1998

Replica Method for Wide Correlators in Gaussian Orthogonal, Unitary And Symplectic Random Matrix Ensembles

We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and wide two-level correlators up to the first nontrivial order O(1/N^2) and wide three-level correlators up to the first nontrivial order $O(1/N^4)$ by carefully treating fluctuations in saddle-point evaluation.

cond-mat↗
arXiv1996

An extended massless phase and the Haldane phase in a spin-1 isotropic antiferromagnetic chain

We study the phase transition of isotropic spin-1 models in the vicinity of the Uimin-Lai-Sutherland model by using the SU(3)_1 WZW model with certain marginal perturbations. The unstable RG trajectory by a marginally relevant perturbation generates a mass gap for the Haldane phase, and thus the universality class of the transition from the massless phase to the Haldane phase at ULS point becomes the BKT type. Our results support recent numerical studies by Fáth and Sólyom. In the massless phase, we calculate logarithmic finite-size corrections of the energy for the SU(ν)-symmetric and asymmetric models.

cond-mat.stat-mech↗
arXiv1995

Renormalization group flow in one- and two-matrix models

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 constants by taking account of reparametrization identities. Despite the nonlinearity of the equation, the location of fixed points and the scaling exponents can be extracted from the equation. They agree with the spectrum of relevant operators in the exact solution. A linearized $β$-function approximates well the global phase structure which includes several nontrivial fixed points. The global renormalization group flow suggests a kind of $c$-theorem in two-dimensional quantum gravity.

hep-th↗
arXiv1994

Random Walk Construction of Spinor Fields on Three Dimensional Lattice

Euclidean invariant Klein-Gordon, Dirac and massive Chern-Simons field theories are constructed in terms of a random walk with a spin factor on a three dimensional lattice. We exactly calculate the free energy and the correlation functions which allow us to obtain the critical diffusion constant and associated critical exponents. It is pointed out that these critical exponents do not satisfy the hyper-scaling relation but the scaling inequalities. We take the continuum limit of this theory on the basis of these analyses. We check the universality of obtained results on other lattice structure such as triclinic lattice and body centered lattice.

hep-th↗
arXiv1994

Quantum Diffusion Process with a Complex Weight on Three Dimensional Lattice

A rigorous definition of a path integral for a spinning particle in three dimensions is given on a regular cubic lattice. The critical diffusion constant and the associated critical exponents in each spin are calculated. Continuum field theories such as Klein-Gordon, Dirac and massive Chern-Simons theories are constructed near these critical points. The universality of obtained results is argued on some other lattices.

hep-th↗
arXiv1994

Smooth Paths on Three Dimensional Lattice

A particular class of random walks with a spin factor on a three dimensional cubic lattice is studied. This three dimensional random walk model is a simple generalization of random walk for the two dimensional Ising model. All critical diffusion constants and associated critical exponents are calculated. Continuum field theories such as Klein-Gordon, Dirac and massive Chern-Simons theories are constructed near several critical points.

hep-th↗
arXiv1994

Chen and Itoi Reply

We reply a Comment (hep-th/xxx) on our recent paper published in Phys Rev Lett 72 (1994) 2527-2530. We point out that the author of the Comment overlooks the highly non-trivial Chern-Simons interactions and his hand-waving arguments are totally groundless.

hep-th↗
arXiv1994

Spin Transmutation in (2+1) Dimensions

We study a relativistic anyon model with a spin-$j$ matter field minimally coupled to a statistical gauge potential governed by the Chern-Simons dynamics with a statistical parameter $α$. A spin and statistics transmutation is shown in terms of a continuous random walk method. An integer or odd-half-integer part of $α$ can be reabsorbed by change of $j$. We discuss the equivalence of a large class of (infinite number) Chern-Simons matter models for given $j$ and $α$.

hep-th↗
arXiv1994

Equivalence of Several Chern-Simons Matter Models

Not only does Chern-Simons (CS) coupling characterize statistics, but also spin and scaling dimension of matter fields. We demonstrate spin transmutation in relativistic CS matter theory, and moreover show equivalence of several models. We study CS vector model in some details, which provide consistent check to the assertion of the equivalence.

hep-th↗
arXiv1993

Nonlinear Renormalization Group Equation for Matrix Models

An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining the critical coupling constant and the critical exponent is obtained. As concrete examples, one-matrix models with one and two coupling constants are analyzed and the exact values of the critical coupling constant and the associated critical exponent are found.

hep-th↗
arXiv1993

Renormalization Group Approach to Matrix Models and Vector Models

The renormalization group approach is studied for large $N$ models. The approach of Brézin 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 simpler example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents. A detailed study of the effective renormalization group flow is presented for cases with up to two coupling constants. We draw the two-dimensional flow diagram.

hep-th↗
arXiv1993

Exact Beta Functions in the Vector Model and Renormalization Group Approach

The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents.

hep-th↗