摘要翻译：
综述了近年来在二维模型重整化群(RG)研究过程中所取得的结果。用Pade-Borel-Leroy方法，将二维n向量λ4欧几里得场论的RG函数记为五圈项，并对微扰级数进行了重新求和。对五圈项的解释表明Wilson不动点只作短暂的移动，使它在由晶格计算结果形成的片段之外。这反映了非分析贡献对β-函数的影响。对五圈近似中n=1,n=0和n=-1的临界指数的计算，以及与已知精确值的比较，证实了非解析贡献在二维中是可见的结论。本文还讨论了基于5圈二维RG级数的伪ε展开式的估计。
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英文标题：
《Two-dimensional phase transition models and \lambda \phi^4 field theory》
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作者：
A. I. Sokolov
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：High Energy Physics - Lattice        高能物理-晶格
分类描述：Lattice field theory. Phenomenology from lattice field theory. Algorithms for lattice field theory.  Hardware for lattice field theory.
晶格场论。从晶格场论到现象学。格场论的算法。晶格场论硬件。
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一级分类：Physics        物理学
二级分类：High Energy Physics - Phenomenology        高能物理-现象学
分类描述：Theoretical particle physics and its interrelation with experiment. Prediction of particle physics observables: models, effective field theories, calculation techniques. Particle physics: analysis of theory through experimental results.
理论粒子物理及其与实验的相互关系。粒子物理可观测物的预测：模型，有效场论，计算技术。粒子物理：通过实验结果分析理论。
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一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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英文摘要：
  The overview is given of the results obtained recently in the course of renormalization-group (RG) study of two-dimensional (2D) models. RG functions of the two-dimensional n-vector \lambda \phi^4 Euclidean field theory are written down up to the five-loop terms and perturbative series are resummed by the Pade-Borel-Leroy techniques. An account for the five-loop term is shown to shift the Wilson fixed point only briefly, leaving it outside the segment formed by the results of the lattice calculations. This is argued to reflect the influence of the non-analytical contribution to the \beta-function. The evaluation of the critical exponents for n = 1, n = 0 and n = -1 in the five-loop approximation and comparison of the results with known exact values confirm the conclusion that non-analytical contributions are visible in two dimensions. The estimates obtained on the base of pseudo-\epsilon expansions originating from the 5-loop 2D RG series are also discussed.
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PDF链接：
https://arxiv.org/pdf/706.3494