Acta Physica Academiae Scientiarum Hungaricae 30. (1971)
1971 / 2. szám - T. Siklós: Theory of Anharmonic Crystals in Pseudoharmonic Approximation II. Three-Dimensional Lattice
THEORY OF ANHARMONIC CRYSTALS, II 197 The critical temperature can be obtained as a simultaneous solution of Eqs. (16), (17) and the second derivative of (16): where the function y(oc) is given by (12), (14). The results of numerical solutions of these systems of equations are given in Figs. 1—3. In Fig. 1 the dependence of the pseudoharmonic renormalization of the frequency ocs — <*>jijl0okj at the instability temperature on the reduced pressure P* is presented for some values of X. In Fig. 2 the dependence of the instability temperature xs = @s/co0L on the dimensionless coupling constant X is given for some values of P*. In Fig. 3 the dependence of the instability temperature on the reduced pressure is presented for some values of X. In all Figures the critical curves are denoted by dot-and-dash lines. We do not consider here the case of small values of X < 2 which demands additional calculations. That will be discussed elsewhere. A{2y'(a)-fay"(a)} = 0,3676 I4t dx G(x) лг3 cosh OCX 4 r sinh OCX 4r (18) Fig. 1. The dependence of the pseudoharmonic renormalization of the frequency as = ^kjl^okj on the reduced pressure P* at the instability temperature Acta Physica Academiae Scientiarum Hungaricae 30, 1971