%0 Journal Article %1 Fortuin1972Randomcluster %A Fortuin, C. M. %A Kasteleyn, P. W. %D 1972 %J Physica %K random-cluster-model percolation critical-phenomena lattice-models %N 4 %P 536--564 %R 10.1016/0031-8914(72)90045-6 %T On the random-cluster model %U http://dx.doi.org/10.1016/0031-8914(72)90045-6 %V 57 %X The random-cluster model is defined as a model for phase transitions and other phenomena in lattice systems, or more generally in systems with a graph structure. The model is characterized by a (probability) measure on a graph and a real parameter κ. By specifying the value of κ to 1, 2, 3, 4, … is shown that the model covers the percolation model, the Ising model, the Ashkin-Teller-Potts model with 3, 4, … states per atom, respectively, and thereby, contains information on graph-colouring problems; in the limit κ ↓ 0 it describes linear resistance networks. It is shown that the function which for the random-cluster model plays the role of a partition function, is a generalization of the dichromatic polynomial earlier introduced by Tutte, and related polynomials.

@article{Fortuin1972Randomcluster, abstract = {{The random-cluster model is defined as a model for phase transitions and other phenomena in lattice systems, or more generally in systems with a graph structure. The model is characterized by a (probability) measure on a graph and a real parameter \^{I}º. By specifying the value of \^{I}º to 1, 2, 3, 4, … is shown that the model covers the percolation model, the Ising model, the Ashkin-Teller-Potts model with 3, 4, … states per atom, respectively, and thereby, contains information on graph-colouring problems; in the limit \^{I}º ↓ 0 it describes linear resistance networks. It is shown that the function which for the random-cluster model plays the role of a partition function, is a generalization of the dichromatic polynomial earlier introduced by Tutte, and related polynomials.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Fortuin, C. M. and Kasteleyn, P. W.}, biburl = {https://www.bibsonomy.org/bibtex/227127ddca323724c8e45f8d8b0d277b4/nonancourt}, citeulike-article-id = {1918577}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/0031-8914(72)90045-6}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6X42-46BVYM3-6N/2/7e5582678de82b52f0eb71b8c1689471}, day = 15, doi = {10.1016/0031-8914(72)90045-6}, interhash = {b537118d31b057718a92a4956ccab9f5}, intrahash = {27127ddca323724c8e45f8d8b0d277b4}, issn = {00318914}, journal = {Physica}, keywords = {random-cluster-model percolation critical-phenomena lattice-models}, month = feb, number = 4, pages = {536--564}, posted-at = {2011-05-23 18:18:59}, priority = {2}, timestamp = {2019-08-01T15:36:09.000+0200}, title = {{On the random-cluster model}}, url = {http://dx.doi.org/10.1016/0031-8914(72)90045-6}, volume = 57, year = 1972 }