4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

Details 4D Spin Glasses in Magnetic Field Have a Mean Field like Phase 4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

1997-03-30

arxiv.org/abs/cond-mat/9703253v1

J. Phys. A: Math. Gen. 31 (1998) 1181

Physics

Condensed Matter

Disordered Systems and Neural Networks

Physrev format, 5 ps figures included

Scientific paper

10.1088/0305-4470/31/4/008

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.

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