Studying Phase Transitions By Machine Learning

The main content in this thesis is to study whether machine learning can overtake the traditional physical approaches on application of phase transition problems.We focus on the application of machine learning on two-dimensional square-lattice site percolation problem.Machine learning theory was born in 1950s,which is an interdis-ciplinary subject combined with neurophysiology,statistics and probability,optimazation and computer science.It can be found in various fields for its high accuracy and efficien-cy in identification and classification of big data,such as image recognition,data mining and natural language processing.In recent decades,successful applications in crystal struc-ture prediction by regression,quantum many-body impurity problems and classification of phase transitions have made machine learning gradually become a burgeoning technique to deal with physical problems.Detecting phase transition is the most typical work in the combination of physics and machine learning theory.A fundamental concern for machine learning to study phase transition problem is that whether it can beyond conventional phys-ical approaches.Recent findings indicate that unsupervised learning may achieved such an aim,i.e.,a proper machine learning approach is able to identify the critical point from unla-belled data.We show that this approach is applicable only under the condition that phases can be described exactly by certain statistical indexes,and fails in more general cases such as the percolation phase transition.Hence,supervised learning methods should be used.We present that benefited from the generalization ability,a learning machine trained by su-pervised learning with configurations at a normal phase can finding the critical point from unlabelled configurations.In appendixes,we study the energy transportation problems on two-dimensional mate-rials.In this article we study a two-dimensional crystal lattice model which is constructed by coupled one-dimensional chains with heavy and light atoms alternatively.We report that chains of light atoms have higher heat conductivity than the heavy ones.This fact implies the existence of super channels of heat conduction in complex nanoscale crystals.Further-more,we find that,due to the interactions among heavy and light atoms,heat conduction behaviors of this kind of crystals are qualitatively different from that of the monotonic two-dimensional lattices.How to verify the microscopic heat transport channel is experimentally suggested.Furthermore,we discuss the particle diffusion problem on two-dimensional gases.The most studied equation is the Boltzman equation.Analytic solutions of Boltzman equations on some models are rare to find,such as Maxwell gas and Coulomb gas.However,there is no solution on the most studied model,Lennard-Jones gas,in molecular dynamics yet.In this thesis,we calculates the first order of self-diffusion coefficients of the two-dimensional Lennard-Jones(2,1)gas model and the two-dimensional hard disk model.This results pro-vide a theoretical foundation for latter numerical simulations.