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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?

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  • $\begingroup$ What do you mean by "Can we model random walk for different densities of packing through ising model"? $\endgroup$ – Yvan Velenik Mar 9 '17 at 16:17
  • $\begingroup$ Hello Yvan , i am working on tipping points (phase transition) in ecological systems such as lake system using ising model. Here i am focusing on flow dynamics through vegetation .I want to simulate particle velocity using ising model for different packing of spins (vegetation ) .Hope , i made it clear $\endgroup$ – Curiosity Mar 9 '17 at 23:14
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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)

and

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)

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