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

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 $\rho$ of the long-range interaction, beyond which no critical behavior occurs. The critical threshold value is ${\rho }_c=3/2$, at a difference with the zero field model in which ${\rho }_c=2$. 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.

5 pages, 6 figures

References in corpus (8)

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• Behavior of Ising Spin Glasses in a Magnetic Field
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
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• Critical behavior of the random-field Ising model with long-range interactions in one dimension
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• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• Exact ground states of one-dimensional long-range random-field Ising magnets
• Phase-transitions of the random bond Potts chain with long-range interactions
• Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
• Critical Exponents of the Random Field Hierarchical Model
• Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field)
• Mean-field theory is exact for the random-field model with long-range interactions
• Universal scaling in real dimension
• Critical exponents of the spin glass transition in a field at zero temperature
• Existence of long-range order in random-field Ising model on Dyson hierarchical lattice
• Quasi-one-dimensional Ising models with defects of the "random local field" type: Imry-Ma phase in spaces with dimension higher than the lower critical one
• Statistical mechanics of the spherical hierarchical model with random fields
• Evidence of de Almeida-Thouless line below six dimensions