Constraints on string percolation model from anomalous centrality evolution data in Au-Au collisions at $\mathbf{\sqrt{s_{NN}}=}$ 62 and 200 GeV

Anomalous centrality evolution of two-particle angular correlations observed in Au-Au collisions at $\sqrt{s_{NN}} = 62$ and 200 GeV and the onset of ridge structures are considered in the model of interacting quark-gluon strings. We assume that at the given energy of nucleus-nucleus collisions the critical energy density may be reached at the specific centrality. In a string percolation model this might be treated equivalently to a formation of a large cluster of strings characterized by the critical string density, with a size comparable to the whole area of interaction of two nuclei. This hypothesis allows to define some constraints on the string percolation model using data on transitional centralities in Au-Au collisions at these two energies. Results are extrapolated to the LHC energy where high string densities (exceeding the critical value) are confirmed for all classes of centralities in Pb-Pb collisions. Interaction between strings inside large clusters formed in nucleus-nucleus collisions is considered in a simplified Monte Carlo model. This model is applied to the qualitative analysis of the onset of collectivity and the ridge formation in Pb-Pb collisions. It is shown that the approach of the repulsive string-string interaction is capable to explain the appearance of elliptic and triangular flow observed in nucleus-nucleus collisions at RHIC and LHC energies.