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

摘要

The 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) in order to perform a thorough comparison 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 have different critical exponents. The critical exponents α ', β, γ ' and δ of ordinary liquids and 3-dimensional Ising model are reproduced by several sets of the model parameters, but the resulting range of the Fisher exponent τ is rather narrow and lies between 20/11 and 2. 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. It is also shown that the specially defined index αs' recovers the scaling relations. A thorough analysis of the critical exponents obeying the scaling relations along with the condition αs'>-β is performed. The found solutions enable us to reproduce the critical exponents of the 3-dimensional O(4) spin model and to show that for this case the exponent τ falls almost in the same range of values as for the ordinary liquids.