### 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.

Original language | English (US) |
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Pages (from-to) | 421-440 |

Number of pages | 20 |

Journal | Journal of Statistical Physics |

Volume | 77 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 1994 |

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### Keywords

- Inhomogeneous Ising model
- collective modes
- free-energy functional

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*77*(1-2), 421-440. https://doi.org/10.1007/BF02186850