Crossover to mean-field behavior at marginal dimensionality

Abstract

The effective critical exponent ${\ensuremath{\gamma}}_{\mathrm{eff}}=d\mathrm{ln}\frac{{\ensuremath{\chi}}^{\ensuremath{-}1}}{d}\mathrm{ln}t$, where $\ensuremath{\chi}$ is the magnetic susceptibility and $t=\frac{(T\ensuremath{-}{T}_{c})}{{T}_{c}}$ is the reduced temperature, has been measured for the first time in the broad region $0.001<~t<~25$ in the uniaxial dipolar Ising ferromagnets LiTb${\mathrm{F}}_{4}$ and ${\mathrm{D}\mathrm{y}({\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{S}{\mathrm{O}}_{4})}_{3}$ \ifmmode\cdot\else\textperiodcentered\fi{} 9${\mathrm{H}}_{2}$O. For LiTb${\mathrm{F}}_{4}$ a distinct maximum is found in the $t$ dependence of ${\ensuremath{\gamma}}_{\mathrm{eff}}$ which remains to be explained theoretically in a satisfactory way.