E. Michael and . Fisher, Critical temperatures of anisotropic ising lattices. ii. general upper bounds, Physical Review, vol.162, issue.2, p.480, 1967.

M. Mezard and T. Mora, Constraint satisfaction problems and neural networks: A statistical physics perspective, Journal of Physiology-Paris, vol.103, issue.1-2, pp.107-113, 2009.
DOI : 10.1016/j.jphysparis.2009.05.013

URL : https://hal.archives-ouvertes.fr/hal-00266040

M. J. Wainwright and M. I. Jordan, Graphical Models, Exponential Families, and Variational Inference, Machine Learning, 2008.
DOI : 10.1561/2200000001

D. Koller and N. Friedman, Probabilistic graphical models: principles and techniques, 2009.

D. Greig, . Porteous, H. Allan, and . Seheult, Exact maximum a posteriori estimation for binary images, Journal of the Royal Statistical Society. Series B (Methodological), pp.271-279, 1989.

M. Blatt, S. Wiseman, and E. Domany, Superparamagnetic clustering of data. Physical review letters, p.3251, 1996.

P. John, E. Barton, A. De-leonardis, S. Coucke, and . Cocco, Ace: adaptive cluster expansion for maximum entropy graphical model inference. bioRxiv, p.44677, 2016.

F. Morcos, A. Pagnani, B. Lunt, A. Bertolino, S. Debora et al., Direct-coupling analysis of residue coevolution captures native contacts across many protein families, Proceedings of the National Academy of Sciences, pp.1293-1301, 2011.
DOI : 10.1073/pnas.1111471108

H. David, . Ackley, E. Geoffrey, T. J. Hinton, and . Sejnowski, A learning algorithm for boltzmann machines, Cognitive science, vol.9, issue.1, pp.147-169, 1985.

M. Kac, C. John, and . Ward, A Combinatorial Solution of the Two-Dimensional Ising Model, Physical Review, vol.88, issue.6, p.1332, 1952.
DOI : 10.1103/PhysRev.88.1332

W. Pieter and . Kasteleyn, Dimer statistics and phase transitions, Journal of Mathematical Physics, vol.4, issue.2, pp.287-293, 1963.

E. Michael and . Fisher, On the dimer solution of planar ising models, Journal of Mathematical Physics, vol.7, issue.10, pp.1776-1781, 1966.

N. Nicol, D. Schraudolph, and . Kamenetsky, Efficient exact inference in planar ising models, Advances in Neural Information Processing Systems, pp.1417-1424, 2009.

K. Jason, D. Johnson, M. Oyen, P. Chertkov, and . Netrapalli, Learning planar ising models. arXiv preprint, 2015.

V. Kolmogorov and R. Zabin, What energy functions can be minimized via graph cuts? Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.26, issue.2, pp.147-159, 2004.

Y. Boykov, O. Veksler, and R. Zabih, Fast approximate energy minimization via graph cuts. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.23, issue.11, pp.1222-1239, 2001.

Y. Boykov, O. Veksler, and R. Zabih, Markov random fields with efficient approximations, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231), pp.648-655, 1998.
DOI : 10.1109/CVPR.1998.698673

N. Ruozzi, The bethe partition function of log-supermodular graphical models, Advances in Neural Information Processing Systems, pp.117-125, 2012.

S. Alan, E. B. Willsky, . Sudderth, J. Martin, and . Wainwright, Loop series and bethe variational bounds in attractive graphical models, Advances in neural information processing systems, pp.1425-1432, 2008.

M. Chertkov, Y. Vladimir, and . Chernyak, Loop series for discrete statistical models on graphs, Journal of Statistical Mechanics: Theory and Experiment, vol.2006, issue.06, p.6009, 2006.
DOI : 10.1088/1742-5468/2006/06/P06009

H. Robert, J. Swendsen, and . Wang, Nonuniversal critical dynamics in monte carlo simulations. Physical review letters, p.86, 1987.

U. Wolff, Collective Monte Carlo Updating for Spin Systems, Physical Review Letters, vol.62, issue.4, p.361, 1989.
DOI : 10.1103/PhysRevLett.62.361

M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice, Physical Review E, vol.65, issue.6, p.66127, 2002.
DOI : 10.1103/PhysRevE.65.066127

S. Cocco and R. Monasson, Adaptive cluster expansion for inferring boltzmann machines with noisy data. Physical review letters, p.90601, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00566281

K. Hashimoto, Zeta functions of finite graphs and representations of p-adic groups. Automorphic forms and geometry of arithmetic varieties, pp.211-280, 1989.

F. Krzakala, C. Moore, E. Mossel, J. Neeman, A. Sly et al., Spectral redemption in clustering sparse networks, Proceedings of the National Academy of Sciences, vol.110, issue.52, pp.20935-20940, 2013.
DOI : 10.1073/pnas.1312486110

URL : https://hal.archives-ouvertes.fr/cea-01223434

P. Zhang, Non-backtracking operator for ising model and its application in attractor neural networks, 2014.

A. Saade, M. Lelarge, F. Krzakala, and L. Zdeborová, Clustering from sparse pairwise measurements. arXiv preprint, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01391585

A. Saade, F. Krzakala, and L. Zdeborová, Spectral clustering of graphs with the bethe hessian, Advances in Neural Information Processing Systems, pp.406-414, 2014.
URL : https://hal.archives-ouvertes.fr/cea-01140852

A. Saade, F. Krzakala, and L. Zdeborová, Matrix completion from fewer entries: Spectral detectability and rank estimation, Advances in Neural Information Processing Systems, pp.1261-1269, 2015.
URL : https://hal.archives-ouvertes.fr/cea-01222302

Y. Watanabe and K. Fukumizu, Graph zeta function in the bethe free energy and loopy belief propagation, NIPS, pp.2017-2025, 2009.

E. Michael, . Fisher, S. David, and . Gaunt, Ising model and self-avoiding walks on hypercubical lattices and "high-density" expansions, Physical Review, vol.133, issue.1A, p.224, 1964.

A. Dembo and A. Montanari, Ising models on locally tree-like graphs. The Annals of Applied Probability, pp.565-592, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00290779

S. Dommers, C. Giardinà, and R. Van-der-hofstad, Ising Critical Exponents on Random Trees and Graphs, Communications in Mathematical Physics, vol.132, issue.6, pp.355-395, 2014.
DOI : 10.1007/s00220-014-1992-2

M. Mezard and A. Montanari, Information, physics, and computation, 2009.
DOI : 10.1093/acprof:oso/9780198570837.001.0001

S. Jonathan, . Yedidia, T. William, Y. Freeman, and . Weiss, Bethe free energy, kikuchi approximations , and belief propagation algorithms Advances in neural information processing systems, 2001.

T. Mora, Géométrie et inférence dans l'optimisation et en théorie de l'information, 2007.

F. Ricci-tersenghi, The Bethe approximation for solving the inverse Ising problem: a comparison with other inference methods, Journal of Statistical Mechanics: Theory and Experiment, vol.2012, issue.08, p.8015, 2012.
DOI : 10.1088/1742-5468/2012/08/P08015

T. Preis, P. Virnau, W. Paul, and J. J. Schneider, GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model, Journal of Computational Physics, vol.228, issue.12, pp.4468-4477, 2009.
DOI : 10.1016/j.jcp.2009.03.018