Are there generalised Ising models:

  • The underslying mesh/connectivity is completely arbitrary - non rectangular, 3D...ND, complete connectivity should be possible
  • The interaction potential is completely arbitrary of very general class of function
  • Some kind of directionality should be possible
  • Nonbinary, e.g. fractional spin values should be available

I would like to use phyiscal approach for constructing microscopic models for the macroscopic phenomena in artificial general networks and the usual glass, crystal like Ising model is not usable for general networks.

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    $\begingroup$ To me it's not clear what your question is. Of course, all the generalizations you mention have been investigated, and even still far more general settings. What are you after: a description of the most general setting that can be addressed? This won't be possible. A list of various extensions? This would likely fall into the "big list" type of questions that is not welcome here. And what about the results that you'd need about these more general settings? It is one thing to define more general frameworks and another entirely to establish interesting properties in this greater generality. $\endgroup$ – Yvan Velenik Aug 25 '19 at 11:37
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    $\begingroup$ So, to summarize, I believe that you should reformulate your question in a way that makes it easier to provide a relevant answer. $\endgroup$ – Yvan Velenik Aug 25 '19 at 11:38
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    $\begingroup$ A rather general approach is described in this book. A more gentle, but much less general, description can also be found in Chapter 6 of this book. Note that these books are written for mathematicians and thus require some solid background in maths (the first one especially, the second should be more accessible). $\endgroup$ – Yvan Velenik Sep 1 '19 at 7:15
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    $\begingroup$ Another book that might be somewhat closer to what you need if this one. $\endgroup$ – Yvan Velenik Sep 1 '19 at 7:15
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    $\begingroup$ I am not familiar with the non-rigorous literature, so I let others suggest references if they have some. As you can see, and as I said above, this will quickly fall into a (possibly long) list of references... $\endgroup$ – Yvan Velenik Sep 1 '19 at 7:17

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