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arXiv · 1303.6333

Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field

Luca Leuzzi·Giorgio Parisi
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Abstract

The Ising model in a random field and with power-law decaying ferromagnetic bonds is studied at zero temperature. Comparing the scaling of the energy contributions of the ferromagnetic domain wall flip and of the random field a la Imry-Ma we obtain a threshold value for the power $ρ$ of the long-range interaction, beyond which no critical behavior occurs. The critical threshold value is $ρ_c=3/2$, at a difference with the zero field model in which $ρ_c=2$. This prediction is confirmed by numerical computation of the ground states below, at, and above this threshold value. Some possible implications for the critical behavior of spin-glasses in a field are conjectured.

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Luca Leuzzi, Giorgio Parisi. 2013-03-25. Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field. https://doi.org/10.1103/physrevb.88.224204

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