Abstract:
The influence of the critical fluctuations in the vicinity of the structural phase transition (SPT) on the isotope effect (IE) is studied within the anharmonic model of the high-temperature superconductivity. It is shown that if the superconducting transition temperature $T_c$ is equal to the temperature of SPT, then the IE is determined by the critical exponent $\gamma$. In the case $\gamma<1$ the isotope factor for $T_c$ $(\alpha=-\frac{\partial \ln T_c}{\partial \ln M}$) is equal to one for the structural transition temperature $T_0$ (i.e. $\alpha=\varepsilon$, where $\varepsilon=-\frac{\partial \ln T_0}{\partial \ln M}$), but in the case $\gamma>1$$\alpha=\frac{1}{2}$ (if one neglects Coulomb interaction). This result does not depend on the model for the SPT.
The result is demonstrated by considering the exactly solvable model of the
SPT with $\gamma =2$.
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