多参数Φ^4场论的临界现象和重整化群流
Critical phenomena and renormalization-group flow of multi-parameter Φ^4 field theories
摘要：
在重整化群（RG）方法的框架中，通过研究具有$N$分量基本场的多参数$Φ^4$场论的RG流，可以研究临界现象，该基本场最多包含场的四阶多项式.一些物理上有趣的系统需要$Φ^4$场论与几个二次和四次参数，这主要取决于它们的对称性和在过渡处的破缺模式。他们的RG流的结果适用于无序和/或受挫系统，各向异性磁系统，密度波模型，竞争秩序引起的多临界行为。讨论了多参数$Φ^4$场论中RG流的一般性质。概述了一些物理上有趣的情况下的场论结果，并与其他理论方法和实验进行了比较。最后，我们将这种RG方法应用于研究含有$N_f$轻夸克的QCD有限温度跃迁的性质。
英文摘要：
In the framework of the renormalization-group (RG) approach, critical phenomena can be investigated by studying the RG flow of multi-parameter $Φ^4$ field theories with an $N$-component fundamental field, containing up to 4th-order polynomials of the field. Some physically interesting systems require $Φ^4$ field theories with several quadratic and quartic parameters, depending essentially on their symmetry and symmetry-breaking pattern at the transition. Results for their RG flow apply to disorder and/or frustrated systems, anisotropic magnetic systems, density wave models, competing orderings giving rise to multicritical behaviors. The general properties of the RG flow in multi-parameter $Φ^4$ field theories are discussed. An overview of field-theoretical results for some physically interesting cases is presented, and compared with other theoretical approaches and experiments. Finally, this RG approach is applied to investigate the nature of the finite-temperature transition of QCD with $N_f$ light quarks.
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