二级相变理论和Lifshitz条件不成立的论证

系统的自由能是序参量的泛函。在二级相变点附近,自由能密度是序参量及其关联项的幂次展式。按本文给定的方法,无论关联项是定域还是非定域的,由对自由能的一级变分等于零,都能求得表示平衡态位形的序参量。在求解过程,必须将序参量进行傅氏变换,这与序参量以系统对称群的基函数展开是一致的,由此对二级相变中对称改变进行了分析。利用变分法中极值的充要条件(或充分条件),我们讨论了二级相变过程中状态的稳定性条件。由于我们对自由能求极值时没有略去关联项,因此不存在Lifshitz的对称改变限制条件。这里强调指出:实质上,Lif

ON THE THEORY OF SECOND ORDER PHASE TRANSITION AND AN EXPOSITION ON THE NON-VALIDITY OF LIFSHITZ CONDITION

We assume that the free energy of the system is a functional of order parameter. In the vicinity of second order transition, the free energy density can be expanded as a power series of order parameter as well as its correlation term. Following the pro-cedure given here, for both local and non-local, the order parameter representing equilibrium configuration can be found from the vanishment of the first variation of free energy. In order to find out the solution, it is necessary to carry out Fourier transform for order parameter, and this is identical to expand the order parameter in terms of the base functions of symmetric group of the system. In this way, we analyse the change of symmetry in second order transition.By making use the necessary and sufficient condition (or sufficient condition) for extrema in the variational procedure, the condition of stability for states in second order transition is discussed. Because the correlation term has not been neglected in the procedure of finding extrema, so that the restrictions condition of Lifshitz on sym-metry changing does not come into being. It should be pointed out that, in Lifshitz approach the correlation term is neglected in obtaining the minimum of free energy functional, whereas it is included in discussing the problem of stability. Therefore, Lifshitz's approach is inconsistent in itself. Furthermore, there exists certain kinds of system (such as one component axial vector system), in which the correlation term that leads to the Lifshitz condition cannot be constructed from order parameter. Nevertheless, Lifshitz and others also put restrictions on such system. This is obviously unreasonable. By making use the general theoretical approach described above, we explain the experimental results of phase transition in heavy lanthanide metals at Neel point. It serves as an example to show that there are second order phase transition phenomena for which Lifshitz's approach fails to explain.