The order-disorder phase transition of the Ge(001) surface can be described by taking into account only electrostatic interactions between the asymmetric dimers. The transition fits approximately the two-dimensional Ising universality class and accordingly the critical exponent of the order parameter, β, has a value near 1/8 and is observable from an analysis of diffraction intensities. The charge transfer between the up and down atom of the asymmetric dimer consistent with the observed phase transition temperature is about 0.08e.
Zandvliet, H. J. W., Caspers, W. J., & van Silfhout, A. (1991). Order-disorder phase transition of the Ge(001) surface. Solid state communications, 78(5), 455-458. https://doi.org/10.1016/0038-1098(91)90703-X