Monte Carlo Research On Recursive Percolation

Phase transition is a common phenomenon in nature and an important part of statistical physics.Phase transition exists widely in all branches of science.The study of phase transition is of great significance not only in physics,but also in material science,sociology,finance,thermal engineering,metallurgical engineering,chemical industry and meteorology.Phase transition involves multi-body interaction.With the increase of the number of particles involved in the study,the complexity increases exponentially.It is difficult to achieve high-precision research by ordinary methods.For this reason,Monte Carlo method is introduced to study phase transition numerically with the help of modern computer technology.In this paper,percolation which is a classical model for phase transition problems will be studied innovatively by using Monte Carlo method.Firstly,the background knowledge of phase transition and Monte Carlo method is introduced.Then the percolation model is introduced systematically,and then the recursive percolation of this project is introduced.We determine the percolation thresholds up to n=5 by using Monte Carlo method and give critical exponents for any n.This family of exponents differs from any previously known universality class and cannot be accommodated by existing analytical methods.Finally,this paper summarizes other works published by the author during his reading.