## Basic Aspects of the Quantum Theory of Solids : Order and by Daniel I. Khomskii

By Daniel I. Khomskii

Offers the most innovations and crucial theoretical tools of the trendy quantum thought of solids for graduate scholars and researchers.

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Symmetry considerations are very powerful, and they determine the form of the Landau free energy expansion. In the general treatment one should always keep all the terms allowed by symmetry, even if we do not know in detail the physical mechanisms responsible for their appearance. 22), although we did not specify the type of the order parameter or its dependence on the lattice distortion. Of course, the coefficients of such terms do depend on the microscopic nature of the ordering, and to calculate these coefficients is a separate, often very difficult problem.

Close to it the phase diagram of the system has the form shown in Fig. 9. Here we have marked the second-order phase transition by a bold solid line and the first-order transition by a bold dashed one; thin solid lines are spinodals – the lines of overheating and overcooling. 3 Interaction with other degrees of freedom The Landau method of treating phase transitions is very simple, but extremely powerful. g. 3 Interaction with other degrees of freedom 15 interaction with other degrees of freedom.

Close to Tc , ξ becomes very large both when approaching Tc from below and from above. For T → Tc + 0 the average equilibrium value is η = 0, but there exist fluctuation regions in which order is already established; and ξ (T ) is the typical size of such regions, which tends to infinity for T → Tc . Below Tc there exists long-range order, η = 0, but on approaching Tc from below there appear disordered regions, whose size is again of the order ξ (T ). 5 Fluctuations at the second-order phase transitions 21 It is often convenient to describe fluctuations not in real, but in momentum space.