[统计数据] phi^4模型非扰动重整化的若干问题 [推广有奖]

摘要翻译：
研究了phi^4模型的非扰动重整化。首先，我们只积分出一对具有波矢量+/-q的共轭模。然后我们要寻找RG方程，它描述哈密顿量在壳层λ-dλ<k<λ，其中dλ->0的积分下的变换。我们证明了已知的Wegner-Houghton方程与+/-q积分结果简单叠加的假设是一致的。在U->0的高温相中，重整化作用可以用π4耦合常数u的幂展开。我们将这些展开系数与用图解摄动法精确计算的展开系数进行了比较，发现了一些不一致之处。它引起了一个问题，在什么意义上，韦格纳-霍顿方程是真正精确的。
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英文标题：
《Some aspects of the nonperturbative renormalization of the phi^4 model》
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作者：
J. Kaupuzs
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最新提交年份：
2010
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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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英文摘要：
  A nonperturbative renormalization of the phi^4 model is considered. First we integrate out only a single pair of conjugated modes with wave vectors +/- q. Then we are looking for the RG equation which would describe the transformation of the Hamiltonian under the integration over a shell Lambda - d Lambda < k < Lambda, where d Lambda -> 0. We show that the known Wegner--Houghton equation is consistent with the assumption of a simple superposition of the integration results for +/- q. The renormalized action can be expanded in powers of the phi^4 coupling constant u in the high temperature phase at u -> 0. We compare the expansion coefficients with those exactly calculated by the diagrammatic perturbative method, and find some inconsistency. It causes a question in which sense the Wegner-Houghton equation is really exact.
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PDF链接：
https://arxiv.org/pdf/704.0142