Ising models on locally tree-like graphs

@misc{citeulike:2796814, abstract = {We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the `cavity' prediction for the limiting free energy per spin is correct for any temperature and external field. Further, local marginals can be approximated by iterating a set of mean field (cavity) equations. Both results are achieved by proving the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on the appropriate infinite random tree.}, author = {Dembo, Amir and Montanari, Andrea }, citeulike-article-id = {2796814}, eprint = {0804.4726}, keywords = {cavity, graph, ising-model, statistical-mechanics, tree}, month = {May}, posted-at = {2008-05-14 07:34:58}, priority = {2}, title = {Ising models on locally tree-like graphs}, url = {http://arxiv.org/abs/0804.4726}, year = {2008} }

TY - ELEC ID - citeulike:2796814 L3 - citeulike-article-id:2796814 TI - Ising models on locally tree-like graphs N2 - We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the `cavity' prediction for the limiting free energy per spin is correct for any temperature and external field. Further, local marginals can be approximated by iterating a set of mean field (cavity) equations. Both results are achieved by proving the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on the appropriate infinite random tree. KW - cavity KW - graph KW - ising-model KW - statistical-mechanics KW - tree AU - Dembo, Amir AU - Montanari, Andrea PY - 2008/May/01/ UR - http://arxiv.org/abs/0804.4726 ER -