Zero-temperature spinglass-ferromagnetic transition : scaling analysis of the domain-wall energy

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.

v2=final version, 19 pages, 8 figures

References in corpus (8)

• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Multicritical points for the spin glass models on hierarchical lattices
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Strong disorder fixed points in the two-dimensional random-bond Ising model
• Universality of the glassy transitions in the two-dimensional +- J Ising model
• Critical behavior of interfaces in disordered Potts ferromagnets : statistics of free-energy, energy and interfacial adsorption
• Scaling behavior of domain walls at the T=0 ferromagnet to spin-glass transition
• Disordered Potts model on the diamond hierarchical lattice: Numerically exact treatment in the large-q limit

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