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arXiv 1305.4136cond-mat.stat-mechcond-mat.soft
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玻璃化转变模耦合理论中重正化微扰展开的破裂

Breakdown of a renormalized perturbation expansion around mode-coupling theory of the glass transition

Grzegorz Szamel, Elijah Flenner, Hisao Hayakawa

摘要:

我们分析了一个重正化的微扰膨胀周围的模式耦合理论的玻璃化转变。我们重点研究了不可约记忆函数的长时间极限。我们讨论了这个函数的重正化图解展开,并重新和两个无限类的图。我们表明,由此产生的贡献的不可约的记忆功能发散的模式耦合过渡。通过迭代这些不同的贡献构建的梯形图的进一步再求和给出了一个有限的结果,该结果取消了模式耦合理论的不可约记忆函数的表达。

英文摘要:

We analyze a renormalized perturbation expansion around the mode-coupling theory of the glass transition. We focus on the long-time limit of the irreducible memory function. We discuss a renormalized diagrammatic expansion for this function and re-sum two infinite classes of diagrams. We show that the resulting contributions to the irreducible memory function diverge at the mode-coupling transition. A further re-summation of ladder diagrams constructed by iterating these divergent contributions gives a finite result which cancels the mode-coupling theory's expression for the irreducible memory function.

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