Zero-temperature spinglass–ferromagnetic transition: Scaling analysis of the domain-wall energy - Archive ouverte HAL Access content directly
Journal Articles Biophysical Reviews and Letters Year : 2014

## Zero-temperature spinglass–ferromagnetic transition: Scaling analysis of the domain-wall energy

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Cécile Monthus

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Thomas Garel
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#### Abstract

For the Ising model with Gaussian random coupling of average $J_0$ and unit variance, the zero-temperature spinglass-ferromagnetic transition as a function of the control parameter $J_0$ can be studied via the size-$L$ dependent renormalized coupling defined as the domain-wall energy $J^R(L) \equiv E_{GS}^{(AF)}(L)-E_{GS}^{(F)}(L)$ (i.e. the difference between the ground state energies corresponding to AntiFerromagnetic and and Ferromagnetic boundary conditions in one direction). We study numerically the critical exponents of this zero-temperature transition within the Migdal-Kadanoff approximation as a function of the dimension $d=2,3,4,5,6$. We then compare with the mean-field spherical model. Our main conclusion is that in low dimensions, the critical stiffness exponent $\theta^c$ is clearly bigger than the spin-glass stiffness exponent $\theta^{SG}$, but that they turn out to coincide in high enough dimension and in the mean-field spherical model. We also discuss the finite-size scaling properties of the averaged value and of the width of the distribution of the renormalized couplings.

#### Domains

Physics [physics]

### Dates and versions

cea-01323246 , version 1 (30-05-2016)

### Identifiers

• HAL Id : cea-01323246 , version 1
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### Cite

Cécile Monthus, Thomas Garel. Zero-temperature spinglass–ferromagnetic transition: Scaling analysis of the domain-wall energy. Biophysical Reviews and Letters, 2014, 89 (18), ⟨10.1103/PhysRevB.89.184408⟩. ⟨cea-01323246⟩

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