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Fractality and other properties of center domains at finite temperature Part 1: SU(3) lattice gauge theory
High Energy Physics - Lattice · Submitted 28 Jan 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The fractal structure of the clusters in the transition region may have implications regarding both the small shear viscosity and the large opacity of the Quark Gluon Plasma observed in heavy-ion collision experiments.
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The abstract, sentence by sentence
Using finite temperature SU(3) lattice gauge theory in the fixed scale approach we analyze center properties of the local Polyakov loop L(x). We construct spatial clusters of points x where the phase of L(x) is near the same center element and study their properties as a function of temperature. We find that below the deconfinement transition the clusters form objects with a fractal dimension D < 3. As the temperature is increased, the largest cluster starts to percolate and its dimensionality approaches D=3. The fractal structure of the clusters in the transition region may have implications regarding both the small shear viscosity and the large opacity of the Quark Gluon Plasma observed in heavy-ion collision experiments.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Using finite temperature SU(3) lattice gauge theory in the fixed scale approach we analyze center properties of the local Polyakov loop L(x). | method 0.66 | 0.93 | 0.03 | asserted 0.71 |
| s1 | We construct spatial clusters of points x where the phase of L(x) is near the same center element and study their properties as a function of temperature. | method 0.85 | 0.95 | 0.04 | asserted 0.88 |
| s2 | We find that below the deconfinement transition the clusters form objects with a fractal dimension D < 3. | result 1.00 | 0.96 | 0.37 | asserted 1.00 |
| s3 | As the temperature is increased, the largest cluster starts to percolate and its dimensionality approaches D=3. | result 1.00 | 0.92 | 0.22 | asserted 1.00 |
| s4 | The fractal structure of the clusters in the transition region may have implications regarding both the small shear viscosity and the large opacity of the Quark Gluon Plasma observed in heavy-ion collision experiments. | interpretation 1.00 | 0.28 | 0.31 | hedged possibility 1.00 |
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Original abstract
Using finite temperature SU(3) lattice gauge theory in the fixed scale approach we analyze center properties of the local Polyakov loop L(x). We construct spatial clusters of points x where the phase of L(x) is near the same center element and study their properties as a function of temperature. We find that below the deconfinement transition the clusters form objects with a fractal dimension D < 3. As the temperature is increased, the largest cluster starts to percolate and its dimensionality approaches D=3. The fractal structure of the clusters in the transition region may have implications regarding both the small shear viscosity and the large opacity of the Quark Gluon Plasma observed in heavy-ion collision experiments.
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References
How the literature uses it
10 arXiv papers cite this in 28 sentences
Papers citing it · 23 sentences without a confident label
Uses its method or tool 1 paper
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A possible way to set $f$ is to prescribe the value that the physical radius $R$ of the largest cluster should take at low temperatures [ref] .
Center clusters in full QCD at finite temperature and background magnetic field · Scale setting · 0.84
Cites it as support 1 paper
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Because Polyakov-loop distributions in the pure gauge gauge theory at finite gauge-coupling furthermore resemble those of the Haar measure with very high accuracy for all temperatures up to the deconfinement transition at $T_c$ [ref] , the midpoint definition ([ref]) remains equally well justified, in fact, for the corresponding low-order moments $⟨L^m L^*^n⟩$ with $m+n <4$ of the Polyakov-loop in the pure gauge theory throughout the confined phase.
Quarks and Triality in a Finite Volume · Effective Polyakov-loop theory and flux-tube model · 0.97
Cites it as background 3 papers
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Another interesting study based on the topological view point is the study of the center clusters and the percolation [ref] .
Persistent homology analysis of deconfinement transition in effective Polyakov-line model · Introduction · 0.94
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This picture of center clusters has been studied in pure gauge theory with two [ref] , with three [ref] and with four colors [ref] , while preliminary results for dynamical quarks have been obtained in Refs. [ref] .
Center clusters in full QCD at finite temperature and background magnetic field · Center clusters · 0.84
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There are several discussions on the center clustering structure of QCD and some related theories [ref] which may be related to the confinement-deconfinement transition and topological structure of the system [ref] .
Information theoretical view of QCD effective model with heavy quarks · Introduction · 0.95
What it cites · 12 sentences without a confident label
Contests 1 paper
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The mean free path, however, does not equal the average cluster size, as was assumed in Ref. [ref] , since, as we have seen, the clusters are fractal objects.
Center Domains and their Phenomenological Consequences · Summary and discussion · contest 0.75
Uses data or values from 1 paper
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Let us briefly recall an important fact from percolation theory: For random site percolation in 3 dimensions (i.e., all sites of a cubic lattice are occupied with probability $p$ and occupied neighbors are assigned to the same cluster) the critical probability where percolation sets in is $p_c = 0.3116$ [ref] .
Bond and Site Percolation in Three Dimensions · Properties of local Polyakov loops · 0.84
Compares with 1 paper
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At moderate temperatures above $T_c$ this deviation is considerably more pronounced for the phases (compare also Ref. [ref] ), and the distributions for the modulus start to show a strong effect only for large temperatures ($T ≳3 T_c$).
Coherent center domains in SU(3) gluodynamics and their percolation at T_c · Properties of local Polyakov loops · 0.98
Cites as background 5 papers
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Some of the efforts for describing properties of the QGP [ref] have revisited an old suggestion [ref] , namely that center domains play a role in QCD phenomenology.
Simulation of Z(3) walls and string production via bubble nucleation in a quark-hadron transition · Introductory remarks · 0.86
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Some of the efforts for describing properties of the QGP [ref] have revisited an old suggestion [ref] , namely that center domains play a role in QCD phenomenology.
Center Domains and their Phenomenological Consequences · Introductory remarks · 0.86
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For the quenched case several studies can be found in the literature [ref] , and preliminary results for full QCD are documented in Ref. [ref] .
Center clusters in the Yang-Mills vacuum · Introductory remarks · 0.92
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