Spectral random walks and line broadening of impurity molecules in an Ising spin glass environment

Transition energy fluctuations in impurity molecules, embedded in an inhomogeneous environment, are investigated within an Ising spin model of the environment. The spatially distributed impurity molecules are assumed to interact with the Ising spin glass through dipole-dipole type of interaction. We calculate the fluctuations in the transition energies of impurity molecules, for different temperatures and various Ising parameters, and find that the spectral distribution of the fluctuations follows approximately a 1/f power law. The fluorescence spectra of the impurity molecules yield microscopic information about domain structures in the Ising environment. In the case of large disorder, the distribution of transition energies shows profiles similar to those observed in single molecule spectroscopy.