Cellular Automation Model Based On The Canonical Ensemble Potts Magnetic System And Its Application

Potts model has been being a wide attention research issue in physics community, because of its rich in physics content. After in-depth study the phase structure of Potts model with different dimension and different q value, Potts model has become an important testing ground for different methods and approaches in the field of the critical point theory. Up to now, only one-dimensional and two-dimensional Ising model (equivalent to two-state Potts model) can be strictly solved. For multi-dimensional(d>2) Ising model and multi-state Potts model, the analytical theories such as renormalization group method and variational-cumulant expansion method are often used in the study of Potts model, but with the increasing of the state (q value) and the dimension, it will lead to difficulty to get the precise results. Then Monte Carlo simulation has become a main research method. Monte Carlo method puts up sampling experimentation to the thermal equilibrium samples of system, and will get a statistical average of a physical quantity expected. Through using Monte Carlo method to studying Potts model, the phase structure of Potts system is understood in-depth in thermal equilibrium.Besides the nature of Potts system in thermal equilibrium, dynamics model of Potts system became a subject aroused wide attention from peoples. After studying dynamics behavior of system, we can understand the dynamics properties of system and the approaches that the system changes from non-equilibrium to equilibrium. The cellular automaton model is a dynamics model that controlled the evaluation of the state system with the same local rules, which has proved to be a very useful tool for studying dynamical behavior of system. Currently, there exists the investigation about cellular automation model based on the microcanonical ensemble (no energy exchange between system and the outside) Potts system.This thesis puts forward the cellular automation model based on the canonical ensemble (exist energy exchange between the system and the outside) Potts magnetic system. The detailed process is as follows: assign each cellular a possible state q, define the neighbors of each cellular, formulate the local evolution rules, and introduce an interaction of the neighbors and thermal action into the evolution. In this ways, system will organize automatically in accordance with the same evolution rules. For the sake of the more general model, we describe the model based on the non-uniform random distributional canonical ensemble Potts magnetic system, and present the details of implemental and the algorithms.In order to verify the feasibility of the model, we draw the dynamical phase scheme of different shape lattices in Potts system, present the evolution of magneton space configurations in different moments, and compare with the results of predecessors researches.In addition, this thesis is inspired by the irregular Potts model for data clustering algorithm given by Eytan Domany, a Potts magnetic system using cellular automaton model is applied to data clustering. Any testing data regarded as a spin magneton of the Potts system assigned a value, so the entire data set can be seen as a cellular space, where the distance between data points, neighbors of data points and the coupling are defined. Then, under the certain initialization data points evolutes with the same rules, so the evolution of spin magneton can be regarded as automatic data clustering process. It's no need for the entire clustering processes to make any assumptions of data structure of testing data sets. After testing two groups of real data, the results verifies that the automatic clustering method does not require assumptions of data structure for testing data and shows that it fits multi-dimensional data sets, has the characteristics of high precision, and reaches expected purposes.