The Markov Switching Multi-fractal models as a new class of REM-like   models in 1-dimensional space
  We map the Markov Switching Multi-fractal model (MSM) onto the Random Energy Model (REM). The MSM is, like the REM, an exactly solvable model in 1-d space with non-trivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multi-fractal behavior. We also introduce the continuous branching version of the model, calculate the moments and prove multiscaling behavior. Different phases have different multi-scaling properties. 
David B. Saakian
cond-mat.stat-mech cond-mat.dis-nn