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首页> 外文期刊>Journal of Experimental and Theoretical Physics >Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions
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Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions

机译：二维相变的重归一化组函数：奇异贡献问题

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摘要

According to the available publications, the field theoretical renormalization group approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This property is associated with the existence of nonanalytic contributions in the renormalization group functions. The situation is analyzed in this work using a new algorithm for summing divergent series that makes it possible to determine the dependence of the results for the critical exponents on the expansion coefficients for the renormalization group functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonic sections or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in the renormalization group functions.
机译：根据可用的出版物，二维情况下的现场理论重归一化组方法给出的临界指数不同于已知的精确值。此属性与重新规范化组函数中非分析贡献的存在相关。在这项工作中，使用新算法对发散级数求和来分析这种情况，该算法使得可以确定关键指数结果与重新归一化群函数的展开系数的相关性。已经表明，可以通过合理形式的系数函数来获得所有指数的精确值。这些函数具有小的非单调截面或拐点，在自然插值中很难再现。重整化组函数中不必假设存在奇异贡献。

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