241,042 research outputs found
G-algebras, twistings, and equivalences of graded categories
Given Z-graded rings A and B, we study when the categories gr-A and gr-B are
equivalent. We relate the Morita-type results of Ahn-Marki and del Rio to the
twisting systems introduced by Zhang. Using Z-algebras, we obtain a simple
proof of Zhang's main result. This makes the definition of a Zhang twist
extremely natural and extends Zhang's results.Comment: 13 pages; typos corrected and revised slightly; to appear in Algebras
and Representation Theor
Comment on "Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices" [arXiv:0705.1045]
It is shown that a recent article by Z.-D. Zhang [arXiv:0705.1045] is in
error and violates well-known theorems.Comment: LaTeX, 3 pages, no figures, submitted to Philosophical Magazine.
Expanded versio
Universality in two-dimensional Kardar-Parisi-Zhang growth
We analyze simulations results of a model proposed for etching of a
crystalline solid and results of other discrete models in the 2+1-dimensional
Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of
orders n=2,3,4 of the heights distribution are estimated. Results for the
etching model, the ballistic deposition (BD) model and the
temperature-dependent body-centered restricted solid-on-solid model (BCSOS)
suggest the universality of the absolute value of the skewness S = W_3 /
(W_2)^(3/2) and of the value of the kurtosis Q = W_4 / (W_2)^2 - 3. The sign of
the skewness is the same of the parameter \lambda of the KPZ equation which
represents the process in the continuum limit. The best numerical estimates,
obtained from the etching model, are |S| = 0.26 +- 0.01 and Q = 0.134 +- 0.015.
For this model, the roughness exponent \alpha = 0.383 +- 0.008 is obtained,
accounting for a constant correction term (intrinsic width) in the scaling of
the squared interface width. This value is slightly below previous estimates of
extensive simulations and rules out the proposal of the exact value \alpha=2/5.
The conclusion is supported by results for the ballistic deposition model.
Independent estimates of the dynamical exponent and of the growth exponent are
1.605 <= z <= 1.64 and \beta = 0.229 +- 0.005, respectively, which are
consistent with the relations \alpha + z = 2 and z = \alpha / \beta.Comment: 8 pages, 9 figures, to be published in Phys. Rev.
A Generalized Positive Energy Theorem for Spaces with Asymptotic SUSY Compactification
A generalized positive energy theorem for spaces with asymptotic SUSY
compactification involving non-symmetric data is proved. This work is motivated
by the work of Dai [D1][D2], Hertog-Horowitz-Maeda [HHM], and Zhang [Z].Comment: 13 pages, without figures; Some errors are correcte
Universality classes of the Kardar-Parisi-Zhang equation
We re-examine mode-coupling theory for the Kardar-Parisi-Zhang (KPZ) equation
in the strong coupling limit and show that there exists two branches of
solutions. One branch (or universality class) only exists for dimensionalities
and is similar to that found by a variety of analytic approaches,
including replica symmetry breaking and Flory-Imry-Ma arguments. The second
branch exists up to and gives values for the dynamical exponent
similar to those of numerical studies for .Comment: 4 pages, 1 figure, published versio
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