A brief review of the string percolation model and its results are presented together with the comparison to experimental data. First, it is done an introduction to the quark-gluon phase diagram and the lattice results concerning the connement and the percolation of center domains. It is studied the interaction of the strings produced in nucleus-nucleus and proton-proton collisions showing how the string percolation arises. The main consequences of the string percolation, concerning the dependence on the energy and centrality, on the multiplicities and the mean transverse momentum are obtained comparing with experimental data. It is emphasized the non-abelian character of the color eld of the strings forming the cluster to reproduce the rise of the transverse momentum with multiplicity and the relative suppression of multiplicities. It is also studied dierent observables like multiplicity and transverse momentum distributions, dependence with multiplicity and transverse momentum correlations, forward-backward correlations, the strength of the Bose-Einstein correlations, dependence on the multiplicity of J/ψ production and its possible suppression in pp collisions at high multiplicity, strangeness enhancement, elliptic ow, and ridge structure. The comparison with the data shows an overall agreement. The thermodynamical properties of the extended cluster formed in the collision are discussed computing its energy and entropy density, shear viscosity over entropy density ratio, bulk viscosity, sound speed and trace anomaly as a function of temperature, showing a remarkable agreement with lattice QCD evaluations. The string percolation can be regarded as the initial frame able to describe the collective behavior produced in AA and pp collisions.

We study the radial distribution function of the color sources (strings) formed in hadronic collisions and the requirements to obtain a liquid. As a repulsive interaction is needed, we incorporate a concentric core in the strings as well as the probability that a string allows core-core overlaps. We find systems where the difference between the gas-liquid and confined-deconfined phase transition temperatures is small. This explains the experimentally observed liquid behavior of the quark-gluon plasma above the confined-deconfined transition temperature.

We propose a strategy based on the site-bond percolation to minimize the propagation of Phytophthora zoospores on plantations, consisting in introducing physical barriers between neighboring plants. Two clustering processes are distinguished: (i) one of cells with the presence of the pathogen, detected on soil analysis, and (ii) that of diseased plants, revealed from a visual inspection of the plantation. The former is well described by the standard site-bond percolation. In the latter, the percolation threshold is fitted by a Tsallis distribution when no barriers are introduced. We provide, for both cases, the formulas for the minimal barrier density to prevent the emergence of the spanning cluster. Though this work is focused on a specific pathogen, the model presented here can also be applied to prevent the spreading of other pathogens that disseminate, by other means, from one plant to the neighboring ones. Finally, the application of this strategy to three types of commercially important Mexican chili plants is also shown.

We investigate the finite-size effects on the transition temperature associated with the quark-gluon plasma (QGP) formation. From a percolation perspective, the onset of the QGP in high-energy collisions occurs when the spanning cluster of color strings emerges. The principal result presented here is the finite-size effects on the transition temperature expressed as a power law in terms of the nucleon number. We found that the transition temperature is higher for small systems than for large ones. It means that minimal triggering conditions events in pp collisions require about 20 times higher energies than AuAu-PbPb collisions. We also estimate the center-of-mass energy required for the QGP formation as a function of the nucleon number. Our results are consistent with the minimal center-of-mass energies at which the QGP has been observed.

In string percolation model, the study of colliding systems at high energies is based on a continuum percolation theory in two dimensions, where the number of strings distributed in the surface of interest is strongly determined by the size and energy of the colliding particles. It is also expected that the surface where the disks are lying be finite, defining a system without periodic boundary conditions. In this work, we report modifications to the fraction of the area covered by disks in continuum percolating systems due to a finite number of disks and bounded by different geometries: circle, ellipse, triangle, square, and pentagon, which correspond to the first Fourier modes of the shape fluctuation of the initial state after the particle collision. We find that the deviation of the fraction of area covered by disks from its corresponding value in the thermodynamic limit satisfies a universal behavior, where the free parameters depend on the density profile, number of disks, and shape of the boundary. Consequently, it is also found that the color suppression factor of the string percolation model is modified by a damping function related to the small-bounded effects. Corrections to the temperature and the speed of sound defined in string systems are also shown for small and elliptically bounded systems.