Andrea Montanari and Tommaso Rizzo J. Stat. Mech. (2005) P10011 doi:10.1088/1742-5468/2005/10/P10011
Andrea Montanari and Tommaso Rizzo
Show affiliationsWe introduce a method for computing corrections to the Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales.
The derivation of the leading correction is explained and applied to two simple examples: the ferromagnetic Ising model on d-dimensional lattices, and the spin glass on random graphs (both in their high-temperature phases). In the first case we rederive the well known Ginzburg criterion and the upper critical dimension. In the second, we compute finite-size corrections to the free energy.
E-print Number: cond-mat/0506769
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Refers: to
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
75.10.Hk Classical spin models
82B30 Statistical thermodynamics (See also 80-XX)
82B23 Exactly solvable models; Bethe ansatz
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 10 (October 2005)
Received 29 June 2005, accepted for publication 19 September 2005
Published 21 October 2005
Andrea Montanari and Tommaso Rizzo J. Stat. Mech. (2005) P10011
L E Beghian and E Sheldon 2001 J. Phys. A: Math. Gen. 34 2913
Pan Hui and Zhu Jia-Lin 2003 J. Phys.: Condens. Matter 15 7287
Ulvi Yurtsever 1994 Class. Quantum Grav. 11 999
Wu Ya-Bo and Li Jiu-Li 2001 Chinese Phys. Lett. 18 328
A Ashtekar and A Magnon 1984 Class. Quantum Grav. 1 L39
J A Turner et al 1962 J. Sci. Instrum. 39 26
J B Van de Kamer and J J W Lagendijk 2002 Phys. Med. Biol. 47 1827
Hongtao Zhang et al 2009 Nanotechnology 20 385708
Lucien Hardy 2007 J. Phys. A: Math. Theor. 40 3081