NUMERICAL STUDY OF FINITE-TEMPERATURE LATTICE QCD

这项工作旨在通过对晶格上的量子色动力学进行大规模的数值模拟，来阐明从强子相到夸克胶子等离子体相的相变的本质，以及由此产生的高温相的物理性质。在项目的第一年，我们研究了相变本身的性质。在项目的第二年和第三年，我们计算了状态方程，它代表了关于等离子体相的基本信息。我们所取得的主要结果如下：1.为了理解现实世界的有限温度相变，了解上、下夸克m&lt；ud&gt；以及奇异夸克m_S的质量差如何影响相变的性质是非常重要的。我们用柯古特-苏斯金德夸克作用量系统地测定了(m_&lt；ud&gt；，m_S)平面上的相变线，并确定了超过…的临界夸克质量更不存在一级相变。对SU(3)对称情形的进一步研究表明，一阶相变的终点是二阶相变点，在这一点上西格玛粒子变得无质量。以往对夸克胶子等离子体相态方程的计算完全采用Kogut-Susskind夸克作用量。在我们的工作中，我们采用了比Kogut-Susskind夸克作用量自然得多的威尔逊型夸克作用量。由于这个计算是CPU时间密集型的，是一个完整的QCD计算，我们利用了胶子和夸克两个扇区的改进作用。我们采用积分法计算状态方程。对于方法论的准备，我们首先计算了纯规范理论的状态方程，并确定了能量密度和压强与温度的关系。取连续极限，得到的状态方程的结果与标准plqquette作用的结果在3%以内是一致的。对于完整的QCD，我们首先确定了(K，β)平面上的相图，确定了宇称破缺相区和临界线。然后，我们对时间晶格尺寸N1=4和6，空间尺寸大多为16^3的晶格进行了模拟。探索了对应于m_π/m_ρ=0.6-0.95的夸克质量区域，确定了能量密度和压强与温度和夸克质量的函数关系。这些结果的主要特点是：(1)当夸克质量低于m_π/m_ρ=0.9时，只出现弱的依赖关系；(Ii)N_1=6的结果与T/T_1=2以上的连续介质的Stefan-Boltzmann值基本一致。要证实和推广这些结果，还需要进一步的研究，特别是利用更大的时间尺度的晶格进行标度研究。较少

This work aimed to elucidate the nature of the phase transition from hadron phase to quark gluon plasma phase, and physical properties of the consequent high temperature phase, using large-scale numerical simulations of quantum chromodynamics on the lattice. In the first year of the project, we investigated the properties of the phase transition itself. In the second and third years of the project, we calculated the equation of state which represent the fundamental information concerning the plasma phase. The main results we have obtained are as follows.1. For understanding the finite-temperature phase transition of the real world, it is very important to learn how the difference of masses of the up and down quark m_<ud> and that of the strange quark m_s affects the nature of the phase transition. We have carried out a systematic determination of the line of phase transition on the (m_<ud>, m_s) plane using the Kogut-Susskind quark action, and identified the critical quark mass beyond … More which the first-order phase transition becomes absent. Further investigation of the SU (3) symmetric case has shown that the end-point of the first-order transition is a second-order transition point, and that the sigma particle becomes massless at that point.2. Past calculations of the equation of state of the quark gluon plasma phase has exclusively used the Kogut-Susskind quark action. In our work we employed the Wilson-type quark action which is far more natural than the Kogut-Susskind quark action in the spin-flavor content. Since this calculation is CPU time intensive, being a full QCD calculation, we have exploited the use of improved actions both for the gluon and quark sectors. We adopted the integral method for calcuation of equation of state. For a methodological preparation, we first calculated the equation of state for pure gauge theory, and determined the temperature dependence of energy density and pressure. Taking the continuum limit, we obtained results for the equation of state which are in agreement with those of the standard plqquette action within 3%. For full QCD, we first determined the phase diagram on the (K,β) plane, identifying the region of parity broken phase and the critical line. We then carried out simulations on lattices with the temporal lattice size N_1=4 and 6 and the spatical size mostly 16^3. The region of quark masses corresponding to m_π/m_ρ=O.6-0.95 were explored, and the energy density and pressure were determined as a function of temperature and quark mass. The main features found in these results are (i) only weak dependence is seen once quark mass falls below m_π/m_ρ=0.9, and (ii) N_1=6 results show an approximate agreement with the continuum Stefan-Boltzmann values above T/ T_1=2. Further studies are needed to confirm and extend these results, in particulr to carry out scaling study using lattices with larger temporal sizes. Less