Locating fixed points in the phase plane.

The critical point is a fixed point in finite-size scaling. To quantify the behavior of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of the fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of the fixed point, which can be a critical point, a point of the first-order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the three-dimensional three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the Beam Energy Scan program of the Relativistic Heavy Ion Collider.

Examining the crossover from the hadronic to partonic phase in QCD.

A mechanism, consistent with color confinement, for the transition between perturbative and physical vacua during the gradual crossover from the hadronic to partonic phase is proposed. The essence of this mechanism is the appearance and growing up of a kind of grape-shape perturbative vacuum inside the physical one. A percolation model based on simple dynamics for parton delocalization is constructed to exhibit this mechanism. The crossover from hadronic matter to sQGP (strongly coupled quark-gluon plasma) as well as the transition from sQGP to weakly coupled quark-gluon plasma with increasing temperature is successfully described by using this model.