Average properties of combinatorial problems and thermodynamics of spin models on graphs TeX Export

@inproceedings{DMTCS-AC0131, abstract = {The study of thermodynamic properties of classical spin models on infinite graphs naturally leads to consider the new combinatorial problems of random-walks and percolation on the average. Indeed, spin models with {\${O(n)}\$} continuous symmetry present spontaneous magnetization only on transient on the average graphs, while models with discrete symmetry (Ising and Potts) are spontaneously magnetized on graphs exhibiting percolation on the average. In this paper we define the combinatorial problems on the average, showing that they give rise to classifications of graph topology which are different from the ones obtained in usual (local) random-walks and percolation. Furthermore, we illustrate the theorem proving the correspondence between Potts model and average percolation.}, author = {Vezzani, Alessandro and Cassi, Davide and Burioni, Raffaella}, booktitle = {Discrete Random Walks, DRW'03}, citeulike-article-id = {616459}, citeulike-linkout-0 = {http://www.dmtcs.org/proceedings/html/dmAC0131.abs.html}, editor = {Banderier, Cyril and Krattenthaler, Christian}, keywords = {graphs, mechanics, percolation, random-walks, statistical}, pages = {333--344}, posted-at = {2006-05-07 16:06:04}, priority = {2}, publisher = {Discrete Mathematics and Theoretical Computer Science}, series = {DMTCS Proceedings}, title = {Average properties of combinatorial problems and thermodynamics of spin models on graphs}, url = {http://www.dmtcs.org/proceedings/html/dmAC0131.abs.html}, volume = {AC}, year = {2003} }

TY - CONF ID - DMTCS-AC0131 L3 - citeulike-article-id:616459 N2 - The study of thermodynamic properties of classical spin models on infinite graphs naturally leads to consider the new combinatorial problems of random-walks and percolation on the average. Indeed, spin models with {${O(n)}$} continuous symmetry present spontaneous magnetization only on transient on the average graphs, while models with discrete symmetry (Ising and Potts) are spontaneously magnetized on graphs exhibiting percolation on the average. In this paper we define the combinatorial problems on the average, showing that they give rise to classifications of graph topology which are different from the ones obtained in usual (local) random-walks and percolation. Furthermore, we illustrate the theorem proving the correspondence between Potts model and average percolation. SE - DMTCS Proceedings EP - 344 TI - Average properties of combinatorial problems and thermodynamics of spin models on graphs PB - Discrete Mathematics and Theoretical Computer Science VL - AC T2 - Discrete Random Walks, DRW'03 SP - 333 KW - graphs KW - mechanics KW - percolation KW - random-walks KW - statistical AU - Vezzani, Alessandro AU - Cassi, Davide AU - Burioni, Raffaella A2 - Banderier, Cyril A2 - Krattenthaler, Christian PY - 2003/// UR - http://www.dmtcs.org/proceedings/html/dmAC0131.abs.html ER -