强耦合Landau-Ginzburg-Wilson模型相变理论的混合团簇+ RG方法
Hybrid cluster+RG approach to the theory of phase transitions in strongly coupled Landau-Ginzburg-Wilson model
摘要：
有人认为，集群方法提供了一个可行的替代威尔逊的动量壳积分技术在重整化的早期阶段，在场论模型与强耦合场，因为这些方法允许系统的会计系统中的所有相互作用，而不管它们的强度。然而，这些方法，仅限于相对较小的空间尺度，所以他们应该补充更传统的重整化组（RG）技术占大尺度的相关性。为了实现这一目标的“层饼”重整化计划早期开发的旋转对称哈密顿已推广到晶格的情况下。RG技术可以自然地与适当修改的聚类方法相结合，使得RG方程仅在存在大尺度波动的情况下使用，而在没有大尺度波动的情况下，该方法简化为传统的聚类方法。作为一个说明性的例子，我们将最简单的单格点集团近似和局域势RG方程应用于简单立方伊辛模型，计算了磁化曲线、临界温度和临界振幅等非普适量。与蒙特卡罗模拟和级数展开结果一致。
英文摘要：
It is argued that cluster methods provide a viable alternative to Wilson's momentum shell integration technique at the early stage of renormalization in the field-theoretic models with strongly coupled fields because these methods allow for systematic accounting of all interactions in the system irrespective of their strength. These methods, however, are restricted to relatively small spatial scales, so they ought to be supplemented with more conventional renormalization-group (RG) techniques to account for large scale correlations. To fulfil this goal a "layer-cake" renormalization scheme earlier developed for rotationally symmetric Hamiltonians has been generalized to the lattice case. The RG technique can be naturally integrated with an appropriately modified cluster method so that the RG equations were used only in the presence of large scale fluctuations, while in their absence the approach reduced to a conventional cluster method. As an illustrative example the simplest single-site cluster approximation together with the local-potential RG equation are applied to simple cubic Ising model to calculate several non-universal quantities such as the magnetization curve, the critical temperature, and some critical amplitudes. Good agreement with Monte Carlo simulations and series expansion results was found.
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