SU(2)格點規範場論於8個flavors之相結構探討

Abstract

本篇論文研究SU(2)格點規範場論於8個flavors之相結構。我們用混合蒙地卡羅來做數值模擬以了解此規範場論。模擬使用plaquette格點規範作用以及未改良staggered費米子。從plaquette分析模擬結果得知有一bulk (non-thermal)相變。藉由冷起動-熱起動模擬以及遲滯研究得知此相變可能是微弱的一階相變。而後進一步從plaquette的易感性與constraint effective potential (CEP)的分析, 結論是此bulk相變為一crossover。另一方面, 從Polyakov loops的分析模擬結果與一個應用CEP的方法, 我們得知局限-非局限相變點附近的相結構特性。最後, 從模擬結果分析Dirac運算子的特徵值光譜, 初步顯示有一手徵相變。為進一步了解 此相變的詳細特性, 我們量測拓墣荷, 此為與chiral Random Matrix Theory做比 較前的第一步。

In this thesis, the bulk (non-thermal) phase structure of SU(2) lattice gauge theory with 8 fermion flavors in the fundamental representation is investigated. The Hybrid Monte Carlo simulations are performed with unimproved staggered fermions and the plaquette gauge action. One bulk phase transition is observed through the measurement of the plaquette. The results of cold-start and hot-start simulations, as well as the hysteresis study, indicate that this transition can be weakly first order. Further verifications, namely the studies of susceptibility and the constraint effective potential (CEP), demonstrate that the bulk transition is a crossover. Using the smeared Polyakov loops, and a method inspired by the CEP, the vacuum structure near the confining-deconfining phase transition point is analyzed. The Dirac operator eigenvalue spectrum is investigated, and the preliminary results show that there is a chiral phase transition. To clarify the properties of this transition, topological charge is measured as the first step to studying chiral Random Matrix Theory.