Folk R, Moser G
Institute for Theoretical Physics, University of Linz, Austria.
Phys Rev Lett. 2003 Jul 18;91(3):030601. doi: 10.1103/PhysRevLett.91.030601. Epub 2003 Jul 15.
We analyze the field theoretic functions of the dynamical model C in two-loop order. Our results correct long-standing errors in these functions published by several authors. We discuss, in particular, the fixed points for the ratio w* of the two time scales involved, as well as their stability. The regions of the "phase diagram," whose axes are the spatial dimension d and number of order parameter components n, correspond to these fixed points; previous authors have found, in addition, an anomalous region in which the scaling properties were unclear. We show that such an anomalous region does not exist. There are only two regions: one with a finite fixed-point w* where the dynamical exponent z=2+alpha/nu, and another where w*=0 and z is equal to the model A value. We show how the one-loop result is recovered from the two-loop result in the limit epsilon=4-d going to zero.
我们在两圈阶次下分析动力学模型C的场论函数。我们的结果纠正了几位作者发表的这些函数中存在已久的错误。我们特别讨论了所涉及的两个时间尺度之比w的不动点及其稳定性。“相图”的区域，其坐标轴为空间维度d和序参量分量数n，对应于这些不动点；此外，先前的作者发现了一个标度性质不明确的反常区域。我们表明这样的反常区域并不存在。只有两个区域：一个具有有限不动点w，其中动力学指数z = 2 + α/ν，另一个区域w* = 0且z等于模型A的值。我们展示了在ε = 4 - d趋于零的极限情况下，如何从两圈结果恢复一圈结果。
