居里点附近立方铁磁体的场论和各向异性
Field theory and anisotropy of cubic ferromagnet near Curie point
摘要：
临界涨落可以改变立方铁磁体在居里点附近的有效各向异性。如果晶体发生相变进入正交相，且初始各向异性不太强，则有效各向异性在T_c处获得普适值A ~* = v ~*/u ~*，其中u ~* 和v ~* 是进入标度状态方程的立方不动点的坐标和非线性各向异性的表达式。本文利用ε-展开和伪ε-展开技术估计了临界点处各向异性参数A的数值。对u*、v* 和A* 的六圈伪$ε$展开式进行Pade重推，得到的估计值A* = 0.13接近于从五圈ε展开式中提取的估计值，但与β函数本身的六圈展开式分析所给出的值A* = 0.089有很大不同。这种差异进行了讨论，其根源被清除。
英文摘要：
Critical fluctuations are known to change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, effective anisotropy acquires at T_c the universal value A* = v*/u* where u* and v* are coordinates of the cubic fixed point entering the scaling equation of state and expressions for nonlinear susceptibilities. In the paper, the numerical value of the anisotropy parameter A at the critical point is estimated using the ε-expansion and pseudo-ε-expansion techniques. Pade resummation of six-loop pseudo-$ε$-expansions for u*, v*, and A* leads to the estimate A* = 0.13 close to that extracted from the five-loop ε-expansion but differing considerably from the value A* = 0.089 given by the analysis of six-loop expansions of the β-functions themselves. This discrepancy is discussed and its roots are cleared up.
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