Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-03-13
Phys. Rev. Lett. 105, 047206 (2010)
Physics
Condensed Matter
Disordered Systems and Neural Networks
4 pages, 2 figures, revtex 4.1, revised version shows no disrepancy between large N results and KTJ
Scientific paper
10.1103/PhysRevLett.105.047206
We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlev\'e $\tau^{IV} [n]$ function in the $n\to 0$ limit. The large $N$ thermodynamics exactly recovers that of Kosterlitz, Thouless and Jones \cite{ktjonesPRL}. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.
Akhanjee Shimul
Rudnick Joseph
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