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 twenty 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.

Phytophthora is one of the most aggressive and worldwide extended phytopathogens that attack plants and trees. Its effects produce tremendous economical losses in agronomy and forestry since no effective fungicide exists. We propose to combine percolation theory with an intercropping sowing configuration as a non-chemical strategy to minimize the dissemination of the pathogen. In this work, we model a plantation as a square lattice where two types of plants are arranged in alternating columns or diagonals, and Phytophthora zoospores are allowed to propagate to the nearest and next-to-nearest neighboring plants. We determine the percolation threshold for each intercropping configuration as a function of the plant’s susceptibilities and the number of inoculated cells at the beginning of the propagation process. The results are presented as phase diagrams where crop densities that prevent the formation of a spanning cluster of susceptible or diseased plants are indicated. The main result is the existence of susceptibility value combinations for which no spanning cluster is formed even if every cell in the plantation is sowed. This finding can be useful in choosing a configuration and density of plants that minimize damages caused by Phytophthora. We illustrate the application of the phase diagrams with the susceptibilities of three plants with a high commercial value.

We investigate the structure of the medium formed in heavy ion collisions using three different models: the Color String Percolation Model (CSPM), the Core–Shell-Color String Percolation Model (CSCSPM), and the Color Glass Condensate (CGC) framework. We analyze the radial distribution function of the transverse representation of color flux tubes in each model to determine the medium’s structure. Our results indicate that the CSPM behaves as an ideal gas, while the CSCSPM exhibits a structural phase transition from a gas-like to a liquid-like structure. Additionally, our analysis of the CGC framework suggests that it produces systems that behave like non-ideal gases for AuAu central collisions at RHIC energies and liquid-like structures for PbPb central collisions at LHC energies.