https://doi.org/10.59132/fi/2026/1/12-18
Izvleček
Dijakinja se je pod mentorstvom učitelja fizike spomladi 2025 ukvarjala z raziskovalno nalogo s področja perkolacijske teorije. Z Monte Carlo simulacijami z računalniškimi programi, ki jih je vnaprej pripravil mentor v programskem jeziku delphi pascal, je raziskovalka preučevala dvodimenzionalne (2D) in tridimenzionalne (3D) mrežne modele, predvsem vpliv velikosti mreže na perkolacijski prag. V skladu s številnimi znanstvenimi raziskavami po svetu je potrdila, da je perkolacijski prehod v bližini perkolacijskega praga vedno ostrejši, ko se velikost mreže v 2D ali 3D povečuje. Sam perkolacijski prag se z velikostjo mreže spreminja razmeroma malo, v 3D pa je bistveno manjši kot v 2D. Naloga je za razumevanje na srednješolskem nivoju zahtevna in primerna le za najbolj nadarjene dijake. Nov prispevek k dobro znani teoriji in raziskovalnim rezultatom je bil kvantitativno ugotavljanje strmine perkolacijske krivulje v točki perkolacijskega praga.
Abstract
Percolation Theory
In the spring of 2025, a gymnasium student conducted research in the field of percolation theory under the supervision of a physics teacher. Using Monte Carlo computer simulations, prepared in advance with Pascal by the supervisor, the researcher examined two-dimensional (2D) and three-dimensional (3D) lattice (grid) models. The study focused on the influence of the grid size on the percolation threshold. Consistent with numerous scientific studies conducted worldwide, the researcher confirmed that the percolation transition near the percolation threshold becomes sharper as the grid size increases in both 2D and 3D environments. Although the percolation threshold itself varies slightly with different grid sizes, it is significantly lower in 3D compared to 2D. The topic is challenging for secondary-school students, making it suitable for the most talented individuals. A novel contribution to the established theory and research findings is the quantitative determination of the steepness of the percolation curve at the percolation threshold.