Abstract
We consider the nearest-neighbor Ising model in thermal equilibrium on a network with no required regularity or symmetry properties. Both coupling strengths and external fields are site-dependent. The objective is to describe this system in terms of a free energy magnetization functional whose conjugate variables are the external fields. For simply connected networks, this inverse problem has a local structure. On generalizing to loops, the local structure remains if the description is expanded in an overcomplete fashion to include a collective amplitude with respect to which the free energy is stationary. For more complex connectivity, a superbond representation is developed in terms of which the system can be described by a combined auxiliary set of branch and node collective variables.
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References
L. Šamaj,Physica A 153:517 (1988).
J. K. Percus,J. Stat. Phys. 55:1263 (1989).
L. Šamaj,J. Phys. (Paris)50:273 (1989).
J. K. Percus and M. Q. Zhang,Phys. Rev. B 38:11737 (1988).
M. Q. Zhang and J. K. Percus,J. Stat. Phys. 56:695 (1989).
L. Šamaj and J. K. Percus,J. Stat. Phys. 73:235 (1993).
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Dedicated to Oliver Penrose, a master of long-range effects in many-body systems.
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Percus, J.K., Šamaj, L. Exact free energy functionals for non-simply-connected lattices. J Stat Phys 77, 421–440 (1994). https://doi.org/10.1007/BF02186850
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DOI: https://doi.org/10.1007/BF02186850