arXiv subjects
Publications and source records attributed to C. Itoi.
We study short-range quantum spin systems with Gaussian disorder. We obtain quantum mechanical extensions of the Ghirlanda-Guerra identities. We discuss properties of overlap spin operators with these identities.
We show that the low-energy physics of the spin-tube model in presence of a critical magnetic field can be described by a broken SU(3) spin chain. Using the Lieb-Schultz-Mattis Theorem we characterize the possible magnetization plateaus and study the critical behavior in the region of transition between the plateaus m=1/2 and m=3/2 by means of renormalization group calculations performed on the bosonized effective continuum field theory. We show that in certain regions of the parameter space of the effective theory the system remains gapless, and we compute the spin-spin correlation functions in these regions. We also discuss the possibility of a plateau at m=1, and show that although there exists in the continuum theory a term that might cause the appearance of a plateau there, such term is unlikely to be relevant. This conjecture is proved by DMRG techniques. The modifications of the three-leg ladder Hamiltonian that might show plateaus at m =1,5/6,7/6 are discussed, and we give the expected form of correlation functions on the m=1 plateau.
We study critical and universal behaviors of unitary invariant non-gaussian random matrix ensembles within the framework of the large-N renormalization group. For a simple double-well model we find an unstable fixed point and a stable inverse-gaussian fixed point. The former is identified as the critical point of single/double-arc phase transition with a discontinuity of the third derivative of the free energy. The latter signifies a novel universality of large-N correlators other than the usual single arc type. This phase structure is consistent with the universality classification of two-level correlators for multiple-arc models by Ambjorn and Akemann. We also establish the stability of the gaussian fixed point in the multi-coupling model.
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 infinitely many induced interactions to a finite number of them. We find a nonlinear RG equation and an algorithm to obtain the fixed points and the scaling exponents. They reproduce the spectrum of relevant operators in the exact solution. The RG flow is visualized by the linear approximation.
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 for neighboring values of $N$. The reparametrization freedom in field space is formulated by means of the loop equation. The reparametrization identities reduce the flow in the infinite dimensional coupling constant space to that in finite dimensions. The matrix model gives a nonlinear differential equation as an effective renormalization group equation. The fixed point and the susceptibility exponents can be determined even for the matrix models in spite of the nonlinearity. They agree with the exact result.