$ϕ^4$理论的大胆图解Monte Carlo研究
Bold Diagrammatic Monte Carlo Study of $ϕ^4$ Theory
摘要：
将重整化过程引入到黑体图蒙特卡罗（BDMC）中，提出了一种研究强耦合区量子场论的方法。BDMC本质上是使用本地Metropolis类型的更新对费曼图进行采样，并且不会受到符号问题的影响。将该方法应用于三维$ϕ^4$理论，分析了该理论的强耦合极限，并证实了非平凡IR不动点的存在性，与前人的研究结果一致。有趣的是，我们发现，大胆的关联函数的Monte Carlo过程的积木，使该计划收敛，不需要进一步的重算方法。
英文摘要：
By incorporating renormalization procedure into Bold Diagrammatic Monte Carlo (BDMC), we propose a method for studying quantum field theories in the strong coupling regime. BDMC essentially samples Feynman diagrams using local Metropolis-type updates and does not suffer from the sign problem. Applying the method to three dimensional $ϕ^4$ theory, we analyze the strong coupling limit of the theory and confirm the existence of a nontrivial IR fixed point in agreement with prior studies. Interestingly, we find that working with bold correlation functions as building blocks of the Monte Carlo procedure, renders the scheme convergent and no further resummation method is needed.
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