Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field

Abstract

The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical -- but not generally accepted -- field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation.

17 pages, 12 figures

References in corpus (10)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis
• Scaling Relations for Logarithmic Corrections
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Critical Dynamics in Glassy Systems
• The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
• Critical Point Scaling of Ising Spin Glasses in a Magnetic Field
• Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass
• Revisiting (logarithmic) scaling relations using renormalization group
• 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)

Cited by in corpus (5)

• Spin-glass dynamics: experiment, theory and simulation
• Evidence that the AT transition disappears below six dimensions
• Critical exponents of the spin glass transition in a field at zero temperature
• Long-range spin glass in a field at zero temperature
• Evidence of de Almeida-Thouless line below six dimensions