臺灣博碩士論文加值系統

在這篇論文裡，我們探討在有限溫度下純 SU(3) 規範場的相變。而我們運用 hybrid Monte Carlo 演算法去模擬在有限溫度下的quenched QCD，其中我們是把威爾遜規範函式放在 16^3 × 6 的格點上。對於純 SU(3) 規範場而言，從波利亞科夫環圈和它的極化率，我們得知臨界溫度 Tc = 274 ± 1 MeV ，其值很接近被廣為接受的數值 Tc ~ 270 MeV 。

In this thesis, we study the finite temperature phase transition of the pure SU(3) gauge theory. We use the hybrid Monte Carlo method to simulate the quenched QCD at finite temperature, with Wilson gauge action on the 16^3 × 6 lattice. From the Polyakov loop and its susceptibility, we determine the value of the critical temperature Tc = 274 ± 1 MeV, in agreement with the widely accepted value of Tc ~ 270 MeV for pure SU(3) gauge theory.

1 Introduction 1
1.1 QCD in the continuum . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Wilson gauge action . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Wilson and Polyakov loops 6
2.1 Wilson loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Polyakov loop and finite temperature phase transition . . . . . . . . . 8
3 Monte Carlo method 11
3.1 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Hybrid Monte Carlo algorithm . . . . . . . . . . . . . . . . . . . . . . 12
4 Data analysis 16
4.1 Statistical analysis of uncorrelated data . . . . . . . . . . . . . . . . . 16
4.2 Autocorrelation of the data from Monte Carlo simulation . . . . . . . 17
5 Simulation details and results 18
5.1 Performance of GSL random number generator . . . . . . . . . . . . 18
5.1.1 Performance of MT19937 for the uniform distribution . . . . . 19
5.1.2 Performance of MT19937 for the Gaussian distribution . . . . 20
5.2 Simulation at weak and strong couplings . . . . . . . . . . . . . . . . 21
5.2.1 Plaquette value at weak coupling . . . . . . . . . . . . . . . . 21
5.2.2 Plaquette value at strong coupling . . . . . . . . . . . . . . . . 22
5.3 Simulation for quenched QCD at finite temperature . . . . . . . . . . 25
5.3.1 Details of the simulation . . . . . . . . . . . . . . . . . . . . . 25
5.3.2 Results of the simulation . . . . . . . . . . . . . . . . . . . . . 27
5.3.3 Discussion of the simulation . . . . . . . . . . . . . . . . . . . 39
6 Conclusion 40
A Euclidean correlators 41
B Relation to statistical mechanics 44
C Formula for Wilson gauge force 46
Bibliography 49

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