Phase Transitions In A Two Dimensional Dilute O(2) Spin Model: A Monte Carlo Study

In this thesis,we study the phase diagram and the probable tricriticality of a dilute O(2) spin model on the square lattice by means of Monte Carlo simulations and finite size scaling methods.We find out that the KT behaviors are associated with low vacancy probability,while the first order transition behaviors happen in high vacancy probability area.Then we fbcus on the mid-area.Our results suggest that a tricritical point exists.The main contents are as fbllows:In chapter one,we review relevant theoretical background,including the mapping from the O(n) spin model onto the O(n) loop model,the criticality and tricriticality of the O(n) loop model,the XY model and KT transition.The motivation of our research is also introduced.In chapter two,we describe the Monte Carlo algorithms applied in our simulations. We use a hybrid algorithm in which Metropolis sweeps alternate with Wolff cluster steps.The cluster algorithm acts on the non-zero spin only.In chapter three,we present the results of our numeric simulations of the dulite O(2) spin model.We find a KT transition line at low vacancy probability and a first order transition line at high vacancy probability.We preliminarily estimate the tricritical point which is located at v_tri=0.915±0.005,T_tri=0.46189±0.00001 and caculate the critical exponents.Furthermore we put forward the next work plan.In chapter fbur,we conclude this thesis.