Ohzeki, MasayukiThomas, Creighton K.Katzgraber, Helmut G.Bombin, H.Martín-Delgado Alcántara, Miguel Ángel2023-06-202023-06-202011-02-011742-546810.1088/1742-5468/2011/02/P02004https://hdl.handle.net/20.500.14352/42825© 2011 IOP Publishing Ltd and SISSA. We would like to thank A. P. Young and H. Nishimori for fruitful discussions. M.O. acknowledges support from the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B) under Grant No. 20740218. He would also like to thank the Texas A&M University Physics and Astronomy Department for their hospitality during a visit. M.A.M-D. and H.B. acknowledge financial support from the Spanish MICINN Grant No. FIS2009-10061, the CAM research consortium QUITEMAD S2009-ESP-1594, the European Commission PICC: FP7 2007-2013 (Grant No. 249958), and UCM-BS Grant No. GICC-910758. H.G.K. acknowledges support from the Swiss National Science Foundation (Grant No. PP002-114713). The authors acknowledge Texas A&M University for access to their hydra and eos cluster, the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources (Ranger Sun Constellation Linux Cluster), the Centro de Supercomputación y Visualización de Madrid (CeSViMa) for access to the magerit cluster, the Barcelona Supercomputing Center for access to the MareNostrum cluster within the Spanish Supercomputing Network and ETH Zurich for CPU time on the Brutus cluster.We study the effects of disorder on the slope of the disorder–temperature phase boundary near the Onsager point (T_(c) = 2.269 . . .) in spin-glass models. So far, studies have focused on marginal or irrelevant cases of disorder. Using duality arguments, as well as exact Pfaffian techniques we reproduce these analytical estimates. In addition, we obtain different estimates for spin-glass models on hierarchical lattices where the effects of disorder are relevant. We show that the phase-boundary slope near the Onsager point can be used to probe for the relevance of disorder effects.engjournal articlehttp://dx.doi.org/10.1088/1742-5468/2011/02/P02004http://iopscience.iop.orghttps://arxiv.org/abs/1009.6015v2open access53Random Ising-modelHierarchical latticesRenormalization-groupMulticritical pointTransitionFerromagnetStatisticsImpuritiesAlgorithmBehavior.Física-Modelos matemáticos