Critical properties of the
Q-state Potts model for dimensions $3\ensuremath{\le}d\ensuremath{\le}6$ are calculated by means of Wilson's exact momentum-space renormalization-group equation. The scaling-field method of Golner and Riedel is used to approximate the functional differential equation by a set of 11 ordinary coupled differential equations. For $d=4\ensuremath{-}\ensuremath{\epsilon}$, lines of critical and tricritical Potts fixed points are found as functions of
Q that annihilate as
Q approaches a critical value ${Q}_{c}=\frac{2+{\ensuremath{\epsilon}}^{2}}{a+O({\ensuremath{\epsilon}}^{3})}$. For
Q>Qc, the Potts transition is first order. Along these fixed lines the critical and tricritical exponents (upper and lower sign, respectively) are to leading order: $\frac{1}{\ensuremath{\nu}}=2\ensuremath{-}\frac{1}{6}[\ensuremath{\epsilon}\ifmmode\pm\else\textpm\fi{}{({\ensuremath{\epsilon}}^{2}\ensuremath{-}a\ensuremath{\delta})}^{\frac{1}{2}}]$, $\frac{\ensuremath{\varphi}}{\ensuremath{\nu}}=\ensuremath{\mp}{({\ensuremath{\epsilon}}^{2}\ensuremath{-}a\ensuremath{\delta})}^{\frac{1}{2}}$, and $\ensuremath{\eta}=\frac{{[\ensuremath{\epsilon}\ifmmode\pm\else\textpm\fi{}{({\ensuremath{\epsilon}}^{2}\ensuremath{-}a\ensuremath{\delta})}^{\frac{1}{2}}]}^{2}}{216}+b\ensuremath{\delta}$, where $\ensuremath{\epsilon}=4\ensuremath{-}d$, $\ensuremath{\delta}=Q\ensuremath{-}2$, and $\ensuremath{\delta}\ensuremath{\le}{\ensuremath{\delta}}_{c}=\frac{{\ensuremath{\epsilon}}^{2}}{a}+O({\ensuremath{\epsilon}}^{3})$. While the form of the $\ensuremath{\epsilon}$ and $\ensuremath{\delta}$ dependences is exact, the coefficients
a and
b cannot be obtained systematically by $\ensuremath{\epsilon}$ expansion, since the upper critical dimensionality of the Potts model is six when $Q\ensuremath{\ne}2$. In our truncation,
a=6.52 and
b=0.065. The results have been extended to dimensions $3.4\ensuremath{\le}d\ensuremath{\lesssim}4$ by solving the renormalization-group equations numerically. The percolation limit of the Potts model,
Q=1, is also investigated and the critical exponents ${\ensuremath{\nu}}^{P},{\ensuremath{\varphi}}^{P}$, and ${\ensuremath{\eta}}^{P}$ determined as functions of dimension for $3\ensuremath{\le}d\ensuremath{\le}6$.
摘要 提出了一种新的变分解的方法求解极化子问题，并归结为解一个非线性的微分积分方程。其数值计算的结果正是过去工作所预期的。 Abstract A new variational method for solving polaron problem is suggested, and the nonlinear differential-integral equation satisfied by variational solution of plolaron has been derived, the numerical result of which is as anticipated by earlier. works. 作者及机构信息 汪克林, 陈庆虎, 完绍龙 1. 中国科学技术大学基础物理中心 基金项目: 国家攀登计划资助课题. Authors and contacts WANG KE-LIN, CHEN QING-HU, WAN SHAO-LONG 1. 中国科学技术大学基础物理中心 参考文献 施引文献
This is the third article in a sequence in which we reexamine the calculation of the critical exponents of the N-vector model from field theory. In the first article we have applied summation methods to the ε-expansion for which new terms have been calculated (up to order ε5). In the second article we have incorporated in the summation method, in the case of Ising-like systems (N = 1), the knowledge of the exact values of exponents in d = 2 dimensions. Since exact values are now also known in the case of polymers (N = 0), we apply here the same method to this case. Moreover, since for the exponent η for N = 1 the results coming from the ε-expansion and perturbation series at fixed dimension are slightly different, we have recalculated the exponents in the latter case using the variant of the summation method developed for the ε-expansion. The results do not change significantly showing both the reliability and the limits of the method.
摘要 用量子理论处理了单原子四能级跃迁模型,研究了自旋交换劈裂对磁光Kerr旋转的影响.结果表明,磁光Kerr转角与电子自旋交换劈裂能之间关系一般是非线性的,仅当交换劈裂能很小时才有线性关系存在 关键词: Kerr转角 / 磁性 / 交换作用 / 劈裂 Abstract Keywords: / / / 作者及机构信息 徐荣青1, 王嘉赋3, 周青春2 (1)华东船舶工业学院电子与信息系,镇江212003; (2)华东船舶工业学院基础学科系,镇江212003; (3)南京大学物理系,南京210093; Authors and contacts Xu Rong-Qing1, Wang Jia-Fu3, Zhou Qing-Chun2 (1)华东船舶工业学院电子与信息系,镇江212003; (2)华东船舶工业学院基础学科系,镇江212003; (3)南京大学物理系,南京210093; 参考文献 施引文献