Incommensurate structures studied by a modified Density Matrix Renormalization Group Method

A modified density matrix renormalization group (DMRG) method is introduced and applied to classical two-dimensional models: the anisotropic triangular nearest- neighbor Ising (ATNNI) model and the anisotropic triangular next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have complex structures and exhibit incommensurate phases. It was found that the incommensurate phase completely separates the disordered phase from one of the commensurate phases, i. e. the non-existence of the Lifshitz point in phase diagrams of both models was confirmed.Comment: 14 pages, 14 figures included in text, LaTeX2e, submitted to PRB, presented at MECO'24 1999 (Wittenberg, Germany

Critical exponents of the two-layer Ising model

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalisation group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction 1.75 with 1.3% deviation.Comment: 7 pages, with 10 figures include

Implication of Compensator Field and Local Scale Invariance in the Standard Model

We introduce Weyl's scale symmetry into the standard model (SM) as a local symmetry. This necessarily introduces gravitational interactions in addition to the local scale invariance group \tilde U(1) and the SM groups SU(3) X SU(2) X U(1). The only other new ingredients are a new scalar field \sigma and the gauge field for \tilde U(1) we call the Weylon. A noteworthy feature is that the system admits the St\" uckelberg-type compensator. The \sigma couples to the scalar curvature as (-\zeta/2) \sigma^2 R, and is in turn related to a St\" uckelberg-type compensator \varphi by \sigma \equiv M_P e^{-\varphi/M_P} with the Planck mass M_P. The particular gauge \varphi = 0 in the St\" uckelberg formalism corresponds to \sigma = M_P, and the Hilbert action is induced automatically. In this sense, our model presents yet another mechanism for breaking scale invariance at the classical level. We show that our model naturally accommodates the chaotic inflation scenario with no extra field.Comment: This work is to be read in conjunction with our recent comments hep-th/0702080, arXiv:0704.1836 [hep-ph] and arXiv:0712.2487 [hep-ph]. The necessary ingredients for describing chaotic inflation in the SM as entertained by Bezrukov and Shaposhnikov [17] have been provided by our original model [8]. We regret their omission in citing our original model [8

Application of the Density Matrix Renormalization Group Method to a Non-Equilibrium Problem

We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile (one-point function). We show that, even with a small number of retained bases, the DMRG calculation is in excellent agreement with the exact solution obtained by the matrix-product-ansatz approach.Comment: 8 pages, LaTeX (using jpsj.sty), 4 non-embedded figures, submitted to J. Phys. Soc. Jp

Aleph_null Hypergravity in Three-Dimensions

We construct hypergravity theory in three-dimensions with the gravitino \psi_{\mu m_1... m_n}{}^A with an arbitrary half-integral spin n+3/2, carrying also the index A for certain real representations of any gauge group G. The possible real representations are restricted by the condition that the matrix representation of all the generators are antisymmetric: (T^I)^{A B} = - (T^I)^{B A}. Since such a real representation can be arbitrarily large, this implies \aleph_0-hypergravity with infinitely many (\aleph_0) extended local hypersymmetries.Comment: 12 pages, no figure

Phase transition of clock models on hyperbolic lattice studied by corner transfer matrix renormalization group method

Two-dimensional ferromagnetic N-state clock models are studied on a hyperbolic lattice represented by tessellation of pentagons. The lattice lies on the hyperbolic plane with a constant negative scalar curvature. We observe the spontaneous magnetization, the internal energy, and the specific heat at the center of sufficiently large systems, where the fixed boundary conditions are imposed, for the cases N>=3 up to N=30. The model with N=3, which is equivalent to the 3-state Potts model on the hyperbolic lattice, exhibits the first order phase transition. A mean-field like phase transition of the second order is observed for the cases N>=4. When N>=5 we observe the Schottky type specific heat below the transition temperature, where its peak hight at low temperatures scales as N^{-2}. From these facts we conclude that the phase transition of classical XY-model deep inside the hyperbolic lattices is not of the Berezinskii-Kosterlitz-Thouless type.Comment: REVTeX style, 4 pages, 6 figures, submitted to Phys. Rev.

Effect of Al addition on microstructure of AZ91D

Casting is a net shape or near net shape forming process so work-hardening will not be applicable for improving properties of magnesium cast alloys. Grain refinement, solid-solution strengthening, precipitation hardening and specially designed heat treatment are the techniques used to enhance the properties of these alloys. This research focusses on grain refinement of magnesium alloy AZ91D, which is a widely used commercial cast alloy. Recently, Al-B based master alloys have shown potential in grain refining AZ91D. A comparative study of the grain refinement of AZ91D by addition of 0.02wt%B, 0.04wt%B, 0.1wt%B, 0.5wt%B and 1.0wt%B of A1-5B master alloy and equivalent amount of solute element aluminium is described in this paper. Hardness profile of AZ91D alloyed with boron and aluminium is compared