Luttinger-Tisza method

Luttinger-Tisza method is burdened by independent minimization variables, while analysis of the values of the Fourier components F k) makes it possible to immediately exclude no less than half of the variable set and to obtain a result much more quickly. Degeneracy of the ground state occurs either due to coincidence of minimal values of Vt (k) at two boundary points of the first Brillouin zone k = b]/2 and k = b2/2, or as a result of the equality Fj (k) = F2 (k) at the same point k = h/2. The natural consequence of the ground state degeneracy is the presence of a Goldstone mode in the spectrum of orientational vibrations.53... 

Let us present the ground state characteristics of dipoles (interacting as defined by Eq. (2.2.2)) on square, triangular, rectangular, and rhombic lattices. The ground state of a square dipole lattice was first determined by the Luttinger-Tisza method in... 

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