Ising model consists of up spin and down spin or empty/filled space. Can we model random walk for different densities of packing through the Ising model?
There are ways to map the magnetization distribution problem of the Ising model to persistent random walks. The relevant references are:
R. Garcia-Pelayo, "Distribution of magnetization in the finite Ising chain," Journal of Mathematical Physics 50, 013301 (2009)
T. Antal, M. Droz, and Z. Racz, "Probability distribution of magnetization in the one-dimensional Ising model: effects of boundary conditions," Journal of Physics A: Mathematics and General 37, 1465 (2004)