Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical integration of KPZ equation with restrictions   In this paper, we introduce a novel integration method of Kardar-Parisi-Zhang
(KPZ) equation. It has always been known that if during the discrete
integration of the KPZ equation the nearest-neighbor height-difference exceeds
a critical value, an instability appears and the integration diverges. One way
to avoid these instabilities is to replace the KPZ nonlinear-term by a function
of the same term that depends on a single adjustable parameter which is able to
control pillars or grooves growing on the interface. Here, we propose a
different integration method which consists of directly limiting the value
taken by the KPZ nonlinearity, thereby imposing a restriction rule that is
applied in each integration time-step, as if it were the growth rule of a
restricted discrete model, e.g. restricted-solid-on-solid (RSOS). Taking the
discrete KPZ equation with restrictions to its dimensionless version, the
integration depends on three parameters: the coupling constant $g$, the inverse
of the time-step $k$, and the restriction constant $\varepsilon$ which is
chosen to eliminate divergences while keeping all the properties of the
continuous KPZ equation. We study in detail the conditions in the parameters'
space that avoids divergences in the 1-dimensional integration and reproduce
the scaling properties of the continuous KPZ with a particular parameter set.
We apply the tested methodology to the $d$-dimensional case ($d = 3,4$) with
the purpose of obtaining the growth exponent $\beta$, by establishing the
conditions of the coupling constant $g$ under which we recover known values
reached by other authors, in particular for the RSOS model. This method allows
us to infer that $d = 4$ is not the critical dimension of the KPZ universality
class, where the strong-coupling phase dissapears.

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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th