N=4 Supersymmetric Yang-Mills Multiplet in Non-Adjoint Representations

We formulate a theory for N=4 supersymmetric Yang-Mills multiplet in a non-adjoint representation R of SO(N) as an important application of our recently-proposed model for N=1 supersymmetry. This system is obtained by dimensional reduction from an N=1 supersymmetric Yang-Mills multiplet in non-adjoint representation in ten dimensions. The consistency with supersymmetry requires that the non-adjoint representation R with the indices i, j, ... satisfy the three conditions \eta^{i j} = \delta^{i j}, (T^I)^{i j} = - (T^I)^{j i} and (T^I)^{[ i j |} (T^I)^{| k ] l} = 0 for the metric \eta^{i j} and the generators T^I, which are the same as the N=1 case.Comment: 6 pages, no figures, accepted for publication in Phys. Rev.

Phase Diagram of a 2D Vertex Model

Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $\beta = 1/8$ and $\alpha = 0$.Comment: 2 pages, 5 figures, short not

Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.Comment: 15 pages, uses IOP styl

Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group

We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer matrix renormalization group (CTMRG), a variant of the density matrix renormalization group (DMRG), is used for the numerical calculation. The matrix product structure of the variational state in CTMRG makes it possible to stochastically fix spins each by each according to the conditional probability with respect to its environment.Comment: 4 pages, 8figure

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 Point of a Symmetric Vertex Model

We study a symmetric vertex model, that allows 10 vertex configurations, by use of the corner transfer matrix renormalization group (CTMRG), a variant of DMRG. The model has a critical point that belongs to the Ising universality class.Comment: 2 pages, 6 figures, short not

Self-Dual Yang-Mills and Vector-Spinor Fields, Nilpotent Fermionic Symmetry, and Supersymmetric Integrable Systems

We present a system of a self-dual Yang-Mills field and a self-dual vector-spinor field with nilpotent fermionic symmetry (but not supersymmetry) in 2+2 dimensions, that generates supersymmetric integrable systems in lower dimensions. Our field content is (A_\mu{}^I, \psi_\mu{}^I, \chi^{I J}), where I and J are the adjoint indices of arbitrary gauge group. The \chi^{I J} is a Stueckelberg field for consistency. The system has local nilpotent fermionic symmetry with the algebra \{N_\alpha{}^I, N_\beta{}^J \} = 0. This system generates supersymmetric Kadomtsev-Petviashvili equations in D=2+1, and supersymmetric Korteweg-de Vries equations in D=1+1 after appropriate dimensional reductions. We also show that a similar self-dual system in seven dimensions generates self-dual system in four dimensions. Based on our results we conjecture that lower-dimensional supersymmetric integral models can be generated by non-supersymmetric self-dual systems in higher dimensions only with nilpotent fermionic symmetries.Comment: 15 pages, no figure