Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series
Centre symmetric 3d effective actions for thermal SU(N) Yang-Mills from strong coupling series
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强耦合级数热 SU(N) Yang-Mills 的中心对称 3d 有效作用
DOI：
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发表时间：
2010
期刊：
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通讯作者：
O. Philipsen
中科院分区：
文献类型：
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作者：
J. Langelage;S. Lottini;O. Philipsen
我们从晶格四维热 SU(N) Yang-Mills 理论出发，通过强耦合展开式，推导了以 Polyakov 环表示的三维 Z(N) 对称有效作用。因此，文献中对应于（空间）强耦合极限的早期动作被扩展了几个更高阶以及附加的相互作用项。我们提供了有效理论与原始热晶格理论参数 Nτ、β 之间的耦合解析映射，可以系统地改进。然后，我们通过有效理论的蒙特卡罗模拟来研究情况 SU(2) 和 SU(3) 的解除限制转变。我们的有效模型分别正确地再现了二阶 3d Ising 和一阶相变。此外，我们计算了临界耦合 βc(Nτ)，并发现与 4d 理论在 Nτ = 4 − 16 的百分之几水平上的模拟结果一致。
We derive three-dimensional, Z(N)-symmetric effective actions in terms of Polyakov loops by means of strong coupling expansions, starting from thermal SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in the literature, corresponding to the (spatial) strong coupling limit, is thus extended by several higher orders, as well as by additional interaction terms. We provide analytic mappings between the couplings of the effective theory and the parameters Nτ, β of the original thermal lattice theory, which can be systematically improved. We then investigate the deconfinement transition for the cases SU(2) and SU(3) by means of Monte Carlo simulations of the effective theory. Our effective models correctly reproduce second order 3d Ising and first order phase transitions, respectively. Furthermore, we calculate the critical couplings βc(Nτ) and find agreement with results from simulations of the 4d theory at the few percent level for Nτ = 4 − 16.