Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-12-26
J. Stat. Mech. (2009) P03010
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages, 4 figures
Scientific paper
10.1088/1742-5468/2009/03/P03010
We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the authors in Prog. Theor. Phys. 111, 661 (2004). The expression can be handled both analytically and numerically, which is useful for examining how the analyticity of the moment with respect to the replica numbers, which play the role of powers of the moment, can be broken in the thermodynamic limit. A comparison with a replica method analysis indicates that the analyticity breaking can be regarded as the origin of the one-step replica symmetry breaking. The validity of the expression is also confirmed by numerical methods for finite systems.
Kabashima Yoshiyuki
Ogure Kenzo
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