Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters
  and order-parameter fluctuations   We investigate the dependence of the critical Binder cumulant of the
magnetization and the largest Fortuin-Kasteleyn cluster on the boundary
conditions and aspect ratio of the underlying square Ising lattices. By means
of the Swendsen-Wang algorithm, we generate numerical data for large system
sizes and we perform a detailed finite-size scaling analysis for several values
of the aspect ratio $r$, for both periodic and free boundary conditions. We
estimate the universal probability density functions of the largest
Fortuin-Kasteleyn cluster and we compare it to those of the magnetization at
criticality. It is shown that these probability density functions follow
similar scaling laws, and it is found that the values of the critical Binder
cumulant of the largest Fortuin-Kasteleyn cluster are upper bounds to the
values of the respective order-parameter's cumulant, with a splitting behavior
for large values of the aspect ratio. We also investigate the dependence of the
amplitudes of the magnetization and the largest Fortuin-Kasteleyn cluster on
the aspect ratio and boundary conditions. We find that the associated
exponents, describing the aspect ratio dependencies, are different for the
magnetization and the largest Fortuin-Kasteleyn cluster, but in each case are
independent of boundary conditions.

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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom