A novel mathematical mechanism of the critical endpoint generation

Bugaev, K. A.; Petrov, V. K.; Zinovjev, G.

doi:10.1134/s1547477112030065

Cited by 9 publications

(26 citation statements)

References 24 publications

(81 reference statements)

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“…For a certain value of the baryon chemical potential µ, the reduced CST is positive below this curve (Σ(T < T Σ , µ) > 0) and is negative above it (Σ(T > T Σ , µ) < 0). It is worth to note that, as was indicated in works [23,26,27], the negative values of Σ do not contradict the fundamental physical ideas. Indeed, CST in the grand canonical ensemble determines the surface free energy of a cluster f surf = e surf − T s surf , where e surf and s surf are the surface energy and the entropy, respectively.…”

Section: Qgbm With Surface Tensionmentioning

confidence: 56%

“…The exact solution in М2 was found in [27]. Like the case of М1, the phase structure of М2 includes the hadronic phase and the phases of QGP and QGL.…”

Section: Model With Critical Pointmentioning

confidence: 97%

“…QGBM with surface tension has two versions: the model with tricritical point (TCP) [26] and the model with CP [27]. In what follows, we denote them as М1 and М2, respectively.…”

Section: Qgbm With Surface Tensionmentioning

confidence: 99%

“…It is worth noting that it takes different values in М1 (1 < τ ≤ 2) and М2 (τ > 2). The model is solvable for a wide class of functions u(T, µ) and z Q (T, µ), for which the only restrictions are the boundedness and the double differentiability for any values of arguments [23,26,27]. The meaning of the function z Q (T, µ) consists in that it determines the pressure p Q inside a bag 6) in the PT region (µ > µcep) in М1.…”

Section: Qgbm With Surface Tensionmentioning

confidence: 99%

“…It is worth noting that since the pressure in the system is determined by the most right singularity of the isobaric partition function as p = z * T, this condition is just the Gibbs criterion of phase equilibrium [23,26,27]. Hence, the curve T c (µ) should be identified with the deconfinement PT curve.…”

Section: Qgbm With Surface Tensionmentioning

confidence: 99%

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On the Possible Existence of Non-Fisher Universality Classes

Ivanitskyi

Bugaev

2012

Ukr. J. Phys.

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The critical exponents α, α', β, γ', and δ of the model of quark-gluon bags with surface tension are found as functions of the most general model parameters. Two versions of the model that generate the phase diagram of the strongly interacting matter with critical or tricritical endpoint, respectively, are considered. The analysis of the relations between the critical exponents (scaling laws) shows that the scaling can be violated in a general case. The question whether it is possible to restore the scaling laws with the help of the Fisher definition of the α's exponent and its generalizations α'c and α'm is studied. It is shown that the Fisher scaling relation can be recovered with the help of the generalizations α'c and α'm, whereas no definition of the α' index is able to recover the Griffiths scaling relation in its traditional form. It is explicitly demonstrated that the additional condition α = α' is not sufficient to restore the Griffiths scaling relation in the traditional form. A generalization of this scaling relation which is valid for all known models is suggested. The obtained results allow us to conclude on the possible existence of the non-Fisher universality classes, for which the traditional scaling relations can be violated, whereas the generalized scaling laws can be established.

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Section: Qgbm With Surface Tensionmentioning

confidence: 56%

“…The exact solution in М2 was found in [27]. Like the case of М1, the phase structure of М2 includes the hadronic phase and the phases of QGP and QGL.…”

Section: Model With Critical Pointmentioning

confidence: 97%

“…QGBM with surface tension has two versions: the model with tricritical point (TCP) [26] and the model with CP [27]. In what follows, we denote them as М1 and М2, respectively.…”

Section: Qgbm With Surface Tensionmentioning

confidence: 99%

Section: Qgbm With Surface Tensionmentioning

confidence: 99%

Section: Qgbm With Surface Tensionmentioning

confidence: 99%

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On the Possible Existence of Non-Fisher Universality Classes

Ivanitskyi

Bugaev

2012

Ukr. J. Phys.

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The critical indices of the quark gluon bags with surface tension model with tricritical endpoint

Ivanytskyi

2012

Nuclear Physics A

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str. 14 b , Kiev-03680, UkraineThe critical indices α , β, γ and δ of the Quark Gluon Bags with Surface Tension Model with the tricritical endpoint are calculated as functions of the usual parameters of this model and two newly introduces parameters (indices). They are compared with the critical exponents of other models. It is shown that for the newly introduced indices χ = 0 and ξ T ≤ 1 there is a branch of solutions for which the critical exponents of the present model and the statistical multifragmentation model coincide, otherwise these models belong to different universality classes. It is shown that for realistic values of the parameter κ the critical exponents α , β, γ and δ of simple liquids and 3-dimensional Ising model can be only described by the branch of solutions in which all indices except for α correspond to their values within the statistical multifragmentation model. The scaling relations for the found critical exponents are verified and it is demonstrated that for the standard definition of the index α the Fisher and Griffiths scaling inequalities are not fulfilled for some values of the model parameters, whereas the Liberman scaling inequality is always obeyed. Although it is shown that the specially defined index α s recovers the scaling relations, another possibility, an existence of the non-Fisher universality classes, is also discussed.

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The statistical multifragmentation model for liquid–gas phase transition with a compressible nuclear liquid

Sagun¹,

Ivanytskyi²,

Bugaev

et al. 2014

Nuclear Physics A

148

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We propose a new formulation of the statistical multifragmentation model based on the analysis of the virial expansion for a system of the nuclear fragments of all sizes. The developed model not only enables us to account for short-range repulsion, but also to calculate the surface free energy which is induced by the interaction between the fragments. We propose a new parameterization for the liquid phase pressure which allows us to introduce a compressible nuclear liquid into the statistical multifragmentation model. The resulting model is exactly solvable and has no irregular behavior of the isotherms in the mixed phase region that is typical for mean-field models. The general conditions for the 1-st and 2-nd (or higher) order phase transitions are formulated. It is shown that all endpoints of the present model phase diagram are the tricritical points, if the Fisher exponent τ is in the range 3 2 ≤ τ ≤ 2. The treatment of nuclear liquid compressibility allows us to reduce the tricritical endpoint density of the statistical multifragmentation model to one third of the normal nuclear density. A specific attention is paid to of the fragment size distributions in the region of a negative surface tension at supercritical temperatures.

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A novel mathematical mechanism of the critical endpoint generation

Cited by 9 publications

References 24 publications

On the Possible Existence of Non-Fisher Universality Classes

On the Possible Existence of Non-Fisher Universality Classes

The critical indices of the quark gluon bags with surface tension model with tricritical endpoint

The statistical multifragmentation model for liquid–gas phase transition with a compressible nuclear liquid

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