标题： 临界指数和伪$ε$展开 显示英文标题

标题： Critical exponents and the pseudo-$ε$ expansion

摘要： 我们提出了基于六环重整化群展开得到的三维$\lambda\phi^4$$O(n)$对称模型临界指数的伪$\epsilon$展开式（$\tau$级数）。 对于物理上有兴趣的情况$n = 1$,$n = 2$,$n = 3$和$n = 0$，以及$4 \le n \le 32$，给出了具体的数值结果，以阐明所获得级数的一般性质。 伪$\epsilon$-展开式对于指数$\gamma$和$\alpha$具有小且迅速减小的系数。因此，即使直接求和$\tau$系列也能对临界指数得到合理的估计，而使用 Pade 逼近可以得到高精度的数值结果。相反，标度修正指数$\omega$的伪$\epsilon$展开式的系数在物理值$n$下不表现出任何减小的趋势。但相应的级数是符号交替的，在这种情况下，仅使用简单的 Pade 逼近也足以得到可靠的数值估计。 伪$\epsilon$展开技术因此可以被视为一种特定的重整化群级数求和方法，将其转换为计算上方便的展开式。 显示英文摘要

摘要： We present the pseudo-$\epsilon$ expansions ($\tau$-series) for the critical exponents of a $\lambda\phi^4$ three-dimensional $O(n)$-symmetric model obtained on the basis of six-loop renormalization-group expansions. Concrete numerical results are presented for physically interesting cases $n = 1$, $n = 2$, $n = 3$ and $n = 0$, as well as for $4 \le n \le 32$ in order to clarify the general properties of the obtained series. The pseudo-$\epsilon$-expansions for the exponents $\gamma$ and $\alpha$ have small and rapidly decreasing coefficients. So, even the direct summation of the $\tau$-series leads to fair estimates for critical exponents, while addressing Pade approximants enables one to get high-precision numerical results. In contrast, the coefficients of the pseudo-$\epsilon$ expansion of the scaling correction exponent $\omega$ do not exhibit any tendency to decrease at physical values of $n$. But the corresponding series are sign-alternating, and to obtain reliable numerical estimates, it also suffices to use simple Pad\'e approximants in this case. The pseudo-$\epsilon$ expansion technique can therefore be regarded as a specific resummation method converting divergent renormalization-group series into expansions that are computationally convenient.