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arXiv:cond-mat/9508036 · Physical Review Letters

Numerical Evidence for Spontaneously Broken Replica Symmetry in 3D Spin Glasses

Enzo Marinari, Giorgio Parisi A, Juan Jesus Ruiz-Lorenzo, Félix Ritort

Published Jan 29, 1996• 135 citations
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Abstract

Using numerical simulations of the 3D Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
DOI
10.1103/physrevlett.76.843

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We have studied the Parisi overlap distribution for the three-dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures $T\ensuremath{\simeq}{0.7T}_{c}$ and system sizes up to L=32L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}32L=32, we found a P(q)P(q)P(q) as expected for full Parisi replica-symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behavior in Monte Carlo simulations is due to the fact that all existing simulations are done at temperatures too close to the transition temperature so that system sizes larger than the correlation length have not been achieved.
In ref. cond-mat/9811419 Houdayer and Martin analyze the T=0 3d EA spin glass with a magnetic field BBB. By using a new, powerful method, they determine an effective critical field BcB_cBc​ as a function of the lattice size LLL. They use their results to deduce that the model is behaving like in the droplet approach and not like the mean-field theory. We show here, by using some unpublished data, that this very interesting method and numerical results are completely compatible with the behavior implied by the Replica Symmetry Breaking theory.
Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.