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arXiv · 1805.01228

Computation of the Zero Temperature RSB parameter in Bethe Lattice Spin Glasses

Francesco De Santis·Giorgio Parisi
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Abstract

Bethe Lattice Spin Glasses (BLSG) are models with finite connectivity which undergo a Replica Symmetry Breaking (RSB) phase transition in field, even at zero temperature. The order parameter describing this phase is a function related to the non-trivial organization of the states. We compute numerically the spin glass order parameter at zero temperature in BLSG with coordination number $z=3$ and couplings $J=\pm1$, near the transition. The method is based on a universal formula which relates the order parameter to the joint probability distribution of the energy gaps of the lowest lying states. Such distribution is derived numerically by introducing a convenient bulk perturbation to the Hamiltonian.

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Francesco De Santis, Giorgio Parisi. 2018-05-03. Computation of the Zero Temperature RSB parameter in Bethe Lattice Spin Glasses. https://arxiv.org/abs/1805.01228

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