5,116 research outputs found
Numerical Renormalization Group at Criticality
We apply a recently developed numerical renormalization group, the
corner-transfer-matrix renormalization group (CTMRG), to 2D classical lattice
models at their critical temperatures. It is shown that the combination of
CTMRG and the finite-size scaling analysis gives two independent critical
exponents.Comment: 5 pages, LaTeX, 5 figures available upon reques
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
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
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
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
The Density Matrix Renormalization Group technique with periodic boundary conditions
The Density Matrix Renormalization Group (DMRG) method with periodic boundary
conditions is introduced for two dimensional classical spin models. It is shown
that this method is more suitable for derivation of the properties of infinite
2D systems than the DMRG with open boundary conditions despite the latter
describes much better strips of finite width. For calculation at criticality,
phenomenological renormalization at finite strips is used together with a
criterion for optimum strip width for a given order of approximation. For this
width the critical temperature of 2D Ising model is estimated with seven-digit
accuracy for not too large order of approximation. Similar precision is reached
for critical indices. These results exceed the accuracy of similar calculations
for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.
Microstructure and mechanical properties of hip-consolidated Rene 95 powders
The effects of heat-treatments on the microstructure of P/M Rene 95 (a nickel-based powder metal), consolidated by the hot-isostatic pressing (HIP), were examined. The microstructure of as-HIP'd specimen was characterized by highly serrated grain boundaries. Mechanical tests and microstructural observations reveal that the serrated grain boundaries improved ductility at both room and elevated temperatures by retarding crack propagation along grain boundaries
The Signature Triality of Majorana-Weyl Spacetimes
Higher dimensional Majorana-Weyl spacetimes present space-time dualities
which are induced by the Spin(8) triality automorphisms. Different signature
versions of theories such as 10-dimensional SYM's, superstrings, five-branes,
F-theory, are shown to be interconnected via the S_3 permutation group.
Bilinear and trilinear invariants under space-time triality are introduced and
their possible relevance in building models possessing a space-versus-time
exchange symmetry is discussed. Moreover the Cartan's ``vector/chiral
spinor/antichiral spinor" triality of SO(8) and SO(4,4) is analyzed in detail
and explicit formulas are produced in a Majorana-Weyl basis. This paper is the
extended version of hep-th/9907148.Comment: 28 pages, LaTex. Extended version of hep-th/990714
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