The critical indices of the Quark-Gluon Bags with Surface Tension Model with tricritical endpoint

TL;DR

This paper calculates critical indices of the Quark-Gluon Bags with Surface Tension Model at a tricritical point, compares them with other models, and discusses their universality classes and scaling relations.

Contribution

It introduces new parameters to analyze the critical exponents and compares the model's universality class with statistical multifragmentation and other models.

Findings

Critical exponents depend on model parameters and new indices.

Certain solutions match the universality class of the statistical multifragmentation model.

Scaling relations are verified; some inequalities are violated depending on parameters.

Abstract

The critical indices \alpha', \beta, \gamma' and \delta 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 \chi = 0 and \xi^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 \varkappa the critical exponents \alpha', \beta, \gamma' and \delta of simple liquids and 3-dimensional Ising model can be only described by the branch of solutions in which all indices except for \alpha' 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 \alpha' 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 \alpha'_s recovers the scaling relations, another possibility, an existence of the non-Fisher universality classes, is also discussed.