Blekher, P. M. The Bethe lattice spin glass at zero temperature. (English) Zbl 0719.60123 Ann. Inst. Henri Poincaré, Phys. Théor. 54, No. 1, 89-113 (1991). Summary: We prove the existence of a stable solution of the renormalized fixed point equation for the distribution of the single-site magnetization in the Bethe lattice spin glass at zero temperature. The proof is computer assisted. Cited in 2 Documents MSC: 60K40 Other physical applications of random processes 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:existence of a stable solution; Bethe lattice spin glass at zero temperature × Cite Format Result Cite Review PDF Full Text: Numdam EuDML References: [1] D.J. Thouless , Sprin-Glass on a Bethe Lattice , Phys. Rev. Lett. , Vol. 56 , 1986 , p. 1082 . [2] J.T. Chayes , L. Chayes , J.P. Sethna and D.J. Thouless , A Mean Field Spin-Glass with Short-Range Interactions , Commun. Math. Phys. , Vol. 106 , 1986 , p. 41 . Article | MR 853978 [3] J.M. Carlson , J.T. Chayes , L. Chayes , J.P. Sethna and D.J. Thouless , Europhys. Lett. , Vol. 55 , 1988 , p. 355 . [4] D.J. Thouless and C. Kwon , Ising Spin Glass at Zero Temperature on the Bethe Lattice , Phys. Rev. , B 37 , 1988 , p. 7649 - 7654 . [5] W. Feller , An Introduction to Probability Theory and its Applications , J. Wiley & sons Inc . New York e. a., 1971 . · Zbl 0219.60003 [6] F.R. Gantmacher and M.L. Krein , Oscillatory Matrices and Kernels and Small Oscillations of Mechanical Systems , GITTL , Moscow - Leningrad , 1950 , 359 p. · Zbl 0041.35502 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.