On the Possible Existence of Non-Fisher Universality Classes

Abstract

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.

Hadron resonance gas model with induced surface tension

“…It is necessary to stress that an order of mathematical operations is important now [34]. If, in contrast to the steps above, one explicitly substitutes the excluded volume (4) into expression for pressure (33)…”

“…In contrast to the HRGM the continuous part of the QGBSTM mass-volume spectrum, which describes the large and heavy quark-gluon-plasma bags employs the eigenvolume approximation. Note that this approximation is also used in all models describing the large and heavy quark-gluon-plasma bags [25,26,27,28,29,30,31,32,33]. It is applicable at high energy densities or for η > 0.3 − 0.4, while at low packing fractions one has to employ the excluded volume modes which reproduces the low density virial expansion.…”

Physical properties of Polyakov loop geometrical clusters in SU(2) gluodynamics

“…Despite the success of the QGBST models in describing the critical exponents of some universality classes of spin systems such as the O(2)-O(4) model [20,21] and a novel universality class called "the non-Fisher universality class" [22], it is clear that these phenomenological models are dealing with an oversimplified picture of quark-gluon bags.…”

“…Therefore, in this work we would like to study the deconfinement PT in SU(2) gluodynamics on a finite lattice on the basis of cluster models [8,15,18,19,20,21,22,25,26] which describe the liquid-gas PT. For this purpose we will identify the geometrical clusters (a ĺa Gattringer) formed from the local Polyakov loops (continuously valued spins) and study such important properties of the system as the value of the Fisher topological exponent τ and the temperature dependences of the reduced surface tension σ A and of the reduced chemical potential µ A which is usually generated in finite systems by the interaction between clusters [25,26].…”

Alternative formulation of the induced surface and curvature tensions approach

“…Moreover, the IST EoS has two great advantages over the other versions of the hadron resonance gas model: first, it allows one to easily take into account not only the second virial coefficients, but also the third and the fourth ones, and, second, the number of equations to be solved is two and it does not depend on the number of considered different hard-core radii. However, despite these advantages the IST EoS is valid up to packing fractions η = k V k ρ k = 0.2 − 0.22 [10,13], where V k = 4 3 πR 3 k is the eigenvolume of the k-th sort of particles which have the particle number density ρ k and the hard-core radius R k (for a comparison we mention that the VdW EoS with hard-core repulsion is valid for η ≤ 0.1 − 0.11 [10,13]). Therefore, recently in the IST EoS the curvature term was included and the induce surface and curvature tensions (ISCT) EoS was worked out in Refs.…”