Abstract
Partition functions are an important research object in combinatorics and mathematical physics [Barvinok, 2016]. In this work, we consider the partition function of the Ising antiferromagnet on random regular graphs and characterize its limiting distribution in the replica symmetric phase up to the Kesten-Stigum bound. Our proof relies on a careful execution of the method of moments, spatial mixing arguments and small subgraph conditioning.
The authors thank Amin Coja-Oghlan for helpful discussions and insights. Philipp Loick is supported by DFG CO 646/3. The full version of this extended abstract can be found on arXiv:2103.09775.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barvinok, A.: Combinatorics and Complexity of Partition Functions, vol. 9. Springer, Cham (2016)
Coja-Oghlan, A., Efthymiou, C., Jaafari, N., Kang, M., Kapetanopoulos, T.: Charting the replica symmetric phase. Commun. Math. Phys. 359, 603–698 (2018)
Coja-Oghlan, A., Loick, P., Mezei, B., Sorkin, G.: The Ising antiferromagnet and max cut on random regular graphs. arXiv preprint arXiv:2009.10483 (2020)
Coja-Oghlan, A., Hahn-Klimroth, M., Loick, P., Müller, N., Panagiotou, K., Pasch, M.: Inference and mutual information on random factor graphs. In: Proceedings of 37th International Symposium on Theoretical Aspects of Computer Science (2021)
Greenhill, C., Janson, S., Ruciński, A.: On the number of perfect matchings in random lifts. Comb. Probab. Comput. 19, 791–817 (2010)
Guerra, F., Toninelli, F.: The high temperature region of the Viana-Bray diluted spin glass model. J. Stat. Phys. 115, 531–555 (2004)
Huang, K.: Introduction to Statistical Physics. CRC Press, Boca Raton (2009)
Janson, S.: Random regular graphs: asymptotic distributions and contiguity. Comb. Probab. Comput. 4, 369–405 (1995)
Janson, S., Luczak, T., Rucinski, A.: Random Graphs, vol. 45. Wiley, New York (2011)
Mézard, M., Montanari, A.: Information, Physics and Computation. Oxford University Press, Oxford (2009)
Mossel, E., Neeman, J., Sly, A.: Reconstruction and estimation in the planted partition model. Probab. Theory Relat. Fields 162, 431–461 (2015)
Robinson, R., Wormald, N.: Almost all cubic graphs are Hamiltonian. Random Struct. Algorithms 3, 117–125 (1992)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Fabian, C., Loick, P. (2021). The Ising Antiferromagnet in the Replica Symmetric Phase. In: Nešetřil, J., Perarnau, G., Rué, J., Serra, O. (eds) Extended Abstracts EuroComb 2021. Trends in Mathematics(), vol 14. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-83823-2_47
Download citation
DOI: https://doi.org/10.1007/978-3-030-83823-2_47
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-83822-5
Online ISBN: 978-3-030-83823-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)