Clusters and Ising critical droplets: a renormalisation group approach

Coniglio, Antonio; Klein, Wolfgang

doi:10.1088/0305-4470/13/8/025

Cited by 555 publications

(478 citation statements)

References 17 publications

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“…With a rule for calculating clusters it will be very interesting if the thermal critical point also coincides with the onset of a percolating cluster. This aspect was studied by Coniglio and Klein [140]. They propose that the probability that two nearest bonds have an active bond between them be given by…”

Section: Phase Transition In Lgmmentioning

confidence: 99%

Liquid-Gas Phase Transition in Nuclear Multifragmentation

Gupta

Mekjian

Tsang

2001

Advances in the Physics of Particles and Nuclei

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The equation of state of nuclear matter suggests that at suitable beam energies the disassembling hot system formed in heavy ion collisions will pass through a liquid-gas coexistence region. Searching for the signatures of the phase transition has been a very important focal point of experimental endeavours in heavy-ion collisions, in the last fifteen years. Simultaneously theoretical models have been developed to provide information about the equation of state and reaction mechanisms consistent with the experimental observables.

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Section: Phase Transition In Lgmmentioning

confidence: 99%

Liquid-Gas Phase Transition in Nuclear Multifragmentation

Gupta

Mekjian

Tsang

2001

Advances in the Physics of Particles and Nuclei

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“…It only works, if one uses a proper stochastic definition of clusters. 6,7,8,9 Such so-called Fortuin-Kasteleyn clusters of spins can be obtained from the geometrical spin clusters, which consist of nearest-neighbor sites with their spin variables in the same state, by laying bonds with a certain probability between the nearest neighbors. The resulting Fortuin-Kasteleyn clusters are in general smaller than the geometrical ones and also more loosely connected.…”

Section: Introductionmentioning

confidence: 99%

Vortex-line percolation in the three-dimensional complex∣ψ∣4model

2005

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In discussing the phase transition of the three-dimensional complex |ψ| 4 theory, we study the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using high-precision Monte Carlo techniques we investigate if both of them exhibit the same critical behavior leading to the same critical exponents and hence to a consistent description of the phase transition. Different percolation observables are taken into account and compared with each other. We find that different connectivity definitions for constructing the vortex-loop network lead to different results in the thermodynamic limit, and the percolation thresholds do not coincide with the thermodynamic phase transition point.

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“…Quite recently, numerical simulations [13] have indicated that this is indeed correct. Namely, following [4] one can start from a configuration of L 's and build connected bond clusters of nearest neighbors with like sign of the Polyakov loop by placing bonds with probability 1 − exp{2β eff L i L j }. The cluster size distribution of these bond clusters and the magnetic properties of the loop variables in this joint bond-spin percolation model can be studied as the temperature and system sizes are varied.…”

Section: Introductionmentioning

confidence: 99%

“…It is now well established [1,4,10,12,23] that the characteristics of one system can be completely expressed in terms of the other. In particular the critical behavior (if any) of the spin-system translates directly into critical geometrical behavior in the corresponding random cluster model.…”

Section: Introductionmentioning

confidence: 99%

The random cluster representation for the infinite-spin Ising model: application to QCD pure gauge theory

Blanchard

Chayes²,

Gandolfo

2000

Nuclear Physics B

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Recent advances in high energy QCD experiments probing the deconfinement transition from hadronic to coloured quark matter tend to confirm that perlocation of unbounded quarks could provide a signature of this phase transition. In the strong coupling limit the partition function of SU(2) pure gauge theory can be modeled by that of an infinite spin Ising system with short-range ferromagnetic interactions. We derive the Wolff-random cluster representation for these spin models and show that, at least in these cases, the thermal and geometrical phase transitions indeed coincide. Moreover, our results are presented in a more general setting (e.g., q-states Potts variable and/or long range interactions allowing a generalisation to a variety of physical systems.)

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Clusters and Ising critical droplets: a renormalisation group approach

Cited by 555 publications

References 17 publications

Liquid-Gas Phase Transition in Nuclear Multifragmentation

Liquid-Gas Phase Transition in Nuclear Multifragmentation

Vortex-line percolation in the three-dimensional complex∣ψ∣4model

The random cluster representation for the infinite-spin Ising model: application to QCD pure gauge theory

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