### 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) |
---|---|

Pages (from-to) | 421-440 |

Number of pages | 20 |

Journal | Journal of Statistical Physics |

Volume | 77 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1994 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

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

**Exact free energy functionals for non-simply-connected lattices.** / Percus, Jerome; Šamaj, L.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 77, no. 1-2, pp. 421-440. https://doi.org/10.1007/BF02186850

}

TY - JOUR

T1 - Exact free energy functionals for non-simply-connected lattices

AU - Percus, Jerome

AU - Šamaj, L.

PY - 1994/10

Y1 - 1994/10

N2 - 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.

AB - 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.

KW - collective modes

KW - free-energy functional

KW - Inhomogeneous Ising model

UR - http://www.scopus.com/inward/record.url?scp=21844493452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844493452&partnerID=8YFLogxK

U2 - 10.1007/BF02186850

DO - 10.1007/BF02186850

M3 - Article

VL - 77

SP - 421

EP - 440

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -