Percolation line of self-bound clusters in supercritical fluids

Campi, Xavier; Krivine, H.; Sator, Nicolas

doi:10.1016/s0378-4371(01)00158-3

Cited by 40 publications

(49 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The gas-liquid coexistence curve obtained by Panagiotopoulos 37 and the MC liquid-solid coexistence curve of Hansen and Verlet 38 are also shown. The MD results for the HE criterion are similar to those obtained by Campi et al 30 These authors consider that the system is on the percolation line if the second moment of the cluster size distribution that excludes the largest cluster n ′ (s) reaches its maximum. In Fig.…”

Section: Molecular Dynamics Calculationssupporting

confidence: 83%

“…27 It should be mentioned that the HE criterion has been considered in MD studies of small clusters and the critical percolation behavior of Lennard-Jones fluids by several authors. 28,29,30 It has been suggested that the percolation line-the line that separates the temperature-density phase diagram into percolated and non-percolated states-might be experimentally observable. 30,31 Moreover, cluster analysis based on this criterion seems to be useful in locating the gas-liquid coexistence curve.…”

Section: Introductionmentioning

confidence: 99%

“…28,29,30 It has been suggested that the percolation line-the line that separates the temperature-density phase diagram into percolated and non-percolated states-might be experimentally observable. 30,31 Moreover, cluster analysis based on this criterion seems to be useful in locating the gas-liquid coexistence curve. 30 The main purpose of this work is to apply the generalized connectedness OZ type relationship closed with a connectedness PY condition for the Lennard-Jones fluid in order to obtain the pair connectedness function g † HE (r 1 , r 2 , p 1 , p 2 ) for HE clusters and thus the related cluster pair correlation function:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Pugnaloni

Zarragoicoechea

Vericat

2006

The Journal of Chemical Physics

View full text Add to dashboard Cite

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by T.L. Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick like integral equation for a velocity-averaged version of Hill's energetic criterion.

show abstract

Section: Molecular Dynamics Calculationssupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Pugnaloni

Zarragoicoechea

Vericat

2006

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…and Zipf's laws. As mentioned before, various theories of cluster formation (Fischer droplets [10], lattice-gas [6], Lennard-Jones fluids with Hill's clusters [11], percolation [8]), predict power laws c.s.d. with τ ≃ 2 at the corresponding critical points.…”

mentioning

confidence: 99%

Zipf's law in multifragmentation

Campi

Krivine²

2005

Phys. Rev. C

View full text Add to dashboard Cite

We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent τ ≃ 2. We also recall why the presence of such distribution is not a reliable signal of a liquid-gas phase transition. PACS number(s): 25.70.Pq, 05.70.Jk, 64.60.AkThe search for reliable signatures of the liquid-gas phase transition in nuclear multifragmentation is, both theoretically and experimentally, one of the major issues of this field of physics. The empirical observation that the size distribution of heavier clusters generated in various processes satisfies the so called Zipf's law [1], has raised interest and curiosity. This was first pointed out by Y.G. Ma [2] in the framework of the isospin dependent lattice gas model and more recently seen in nuclear fragmentation data [3,4].In the present context, Zipf's law 1 states that the mean size (mass or charge)s(r) of the largest, second-largest...r-largest clusters, decreases according to their rank r = 1, 2, · · · , n as s(r) ∼ 1/r λ ,

show abstract

“…We will show that the observation of Fisher scaling does not allow to determine the location of the critical point. Critical behaviors are observed on a line at supercritical density [11] which extends inside the coexistence region [12,13] due to finite size effects. We suggest that the inadequacy of the Fisher model to describe the lattice gas phase diagram comes from the Fisher independent cluster hypothesis which should be correct only at low densities and high temperatures ; indeed we demonstrate that the thermodynamics reconstructed from the Fisher partition sum coincides with the exact one only in the low density and high temperature regime.…”

mentioning

confidence: 99%

Scaling in the lattice gas model

et al. 2002

View full text Add to dashboard Cite

A good quality scaling of the cluster size distributions is obtained for the Lattice Gas Model using the Fisher's ansatz for the scaling function. This scaling identifies a pseudo-critical line in the phase diagram of the model that spans the whole (subcritical to supercritical) density range. The independent cluster hypothesis of the Fisher approach is shown to describe correctly the thermodynamics of the lattice only far away from the critical point.PACS numbers: 24.10. Pa,64.60.Fr,68.35.Rh Since the first heavy ion experiments multifragmentation has been tentatively connected to a critical phenomenon [1]. The recent determination of a consistent set of critical exponents in different multifragmentation data [2,3] tends to confirm this hypothesis even if the finite size corrections to scaling are largely unknown. On the other side the experimental observation of a flattening of the caloric curve [4,5] and the measurement of a negative heat capacity [6] points towards a first order phase transition as it is also suggested by the thermodynamics of statistical multifragmentation models [7]. The debate on the order of the transition has been further animated by a very recent analysis of the Isis data [8] which shows a high quality scaling of the fragment size distribution over a wide range of charges and deposited energies with an ansatz for the scaling function taken from the Fisher droplet model [9] which approximates a real fluid as an ideal gas of clusters. The critical temperature extracted from the Fisher analysis is identified as the temperature of the thermodynamical critical point and the whole coexistence line of the nuclear phase diagram is reconstructed under the hypothesis that the Fisher model gives a good description of the multifragmentation phenomenon [8].In this paper we apply the Fisher scaling method of ref.[8] to the Lattice Gas model, which is a well known paradigm of first as well as second order phase transitions [10], the canonical version of this model being isomorphous to the Ising model at fixed magnetization. We will show that the observation of Fisher scaling does not allow to determine the location of the critical point. Critical behaviors are observed on a line at supercritical density [11] which extends inside the coexistence region [12,13] due to finite size effects. We suggest that the inadequacy of the Fisher model to describe the lattice gas phase diagram comes from the Fisher independent cluster hypothesis which should be correct only at low densities and high temperatures ; indeed we demonstrate that the thermodynamics reconstructed from the Fisher partition sum coincides with the exact one only in the low density and high temperature regime.In our implementation of the lattice gas model [10] the N sites of a cubic lattice are characterized by an occupation number n i which is defined as n i = 0(1) for a vacancy FIG. 1: RG scaling from eq.1(figs.1a,1c) and Fisher scaling from eq.2 (figs.1b,1d) of the cluster size distribution in a 8X8X8 cubic lattice at the critical densit...

show abstract

Percolation line of self-bound clusters in supercritical fluids

Cited by 40 publications

References 28 publications

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Zipf's law in multifragmentation

Scaling in the lattice gas model

Contact Info

Product

Resources

About