Critical exponents of the quark-gluon bags model with the critical endpoint

TL;DR

This paper calculates and analyzes the critical exponents of the Quark-Gluon Bags model with a critical endpoint, revealing unique independence from certain parameters and proposing a new definition for the critical index to satisfy scaling inequalities.

Contribution

It introduces a novel approach to defining the critical index ' that restores scaling relations and demonstrates the model's applicability across different universality classes.

Findings

Critical exponents are independent of Fisher exponent  and parameter .

Standard ' definition violates scaling inequalities; a new '_c definition restores them.

The model describes critical behavior across various systems and universality classes.

Abstract

The critical indices \alpha', \beta, \gamma' and \delta of the Quark Gluon Bags with Surface Tension Model that has the critical endpoint are calculated and compared with the exponents of other models. These indices are expressed in terms of the most general parameters of the model. Despite the usual expectations the found critical indices do not depend on the Fisher exponent \tau and on the parameter \varkappa which relates the mean bag surface to its volume. The scaling relations for the obtained critical exponents are verified and it is demonstrated that for the standard definition of the index \alpha' the Fisher and the Griffiths scaling inequalities are not fulfilled in general case, whereas the Liberman scaling inequality is always obeyed. This is not surprising for the phase diagram with the asymmetric properties of pure phases, but the present model also provides us with the first and explicit example that the specially defined index \alpha'_s does not recover the scaling relations as well. Therefore, here we suggest the physically motivated definition of the index \alpha' = \alpha'_c and demonstrate that such a definition recovers the Fisher scaling inequality, while it is shown that the Griffiths inequality should be generalized for the phase diagram with the asymmetric properties. The critical exponents of several systems that belong to different universality classes are successfully described by the parameters of the present model and hence its equation of state can be used for a variety of practical applications.