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Possibly Exact Solution for the Multicritical Point of Finite-Dimensional Spin Glasses
Hidetoshi Nishimori, Koujin Takeda, Tomohiro Sasamoto
After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimens…
Error counting in a quantum error-correcting code and the ground-state energy of a spin glass
Hidetoshi Nishimori, Peter Sollich
Upper and lower bounds are given for the number of equivalence classes of error patterns in the toric code for quantum memory. The results are used to derive a lower bound on the g…
Griffiths inequalities for the Gaussian spin glass
Satoshi Morita, Hidetoshi Nishimori, Pierluigi Contucci
The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using properties of the Gaussian distribution and gauge symmetry of…
Exact Ground-State Energies of the Random-Field Ising Chain and Ladder
Toshiyuki Hamasaki, Hidetoshi Nishimori
We derive the exact ground-state energy of the one-dimensional Ising model in random fields taking values h, 0 and -h with general probabilities. The random-field Ising model on a…