Critical behaviors of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> symmetries in the QCD phase diagram

In this work we have studied the QCD phase structure and critical dynamics related to 3-$d$ $O(4)$ $Z(2)$ symmetry universality classes in two-flavor quark-meson low energy effective theory within functional renormalization group approach. We employed expansion of Chebyshev polynomials solve flow equation for order-parameter potential. The chiral transition line limit, end points explicit breaking are depicted diagram. Various exponents order parameter, susceptibilities correlation lengths been calculated diagram, respectively. find that obtained computation, where a field-dependent mesonic nontrivial dispersion relation is taken into account, quantitative agreement with results from other approaches, e.g., conformal bootstrap, Monte Carlo simulations $d=3$ perturbation expansion, etc. Moreover, size regime diagram found be very small.