Many results of the mean-field theory of spin-glasses violate simple scaling laws, including the magnetic field dependence of the transition lines, crossover effects of random anisotropy, and critical behavior in the ordered phase. These violations arise from two dangerously irrelevant variables. Below eight dimensions some mean-field exponents change and at $d=6$ scaling is restored. Below $d=6$ all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.Many results of the mean-field theory of spin-glasses violate simple scaling laws, including the magnetic field dependence of the transition lines, crossover effects of random anisotropy, and critical behavior in the ordered phase. These violations arise from two dangerously irrelevant variables. Below eight dimensions some mean-field exponents change and at $d=6$ scaling is restored. Below $d=6$ all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.

Physical Review LettersMar 11, 198582 citations

On the critical dynamics of spin-glasses

Vladimir V. Prudnikov, G. B. Teǐtel'Baum

Physics Letters AMar 1, 19771 citation

Scaling theory of the ordered phase of spin glasses

Alan J. Bray, M A Moore

Lecture notes in physicsJan 1, 198782 citations

Renormalization group computation of the critical exponents of hierarchical spin glasses

Michele Castellana, Giorgio Parisi A

The large scale behavior of the simplest non-mean-field spin-glass system is analyzed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the ε-expansion technique with two independent methods. The techniques presented show how the underlying ideas of the renormalization group apply also in this disordered model, in such a way that an ε-expansion can be consistently set up. By pushing such calculation to high orders in ε, a consistent non-mean-field theory for such disordered system could be established, giving a substantial contribution the development of a predictive theory for real spin glasses.The large scale behavior of the simplest non-mean-field spin-glass system is analyzed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the ε-expansion technique with two independent methods. The techniques presented show how the underlying ideas of the renormalization group apply also in this disordered model, in such a way that an ε-expansion can be consistently set up. By pushing such calculation to high orders in ε, a consistent non-mean-field theory for such disordered system could be established, giving a substantial contribution the development of a predictive theory for real spin glasses.

arXiv:1006.5628Physical Review EOct 15, 201036 citations

Absence of an Equilibrium Ferromagnetic Spin-Glass Phase in Three Dimensions

Florent Krząkała, Olivier Martin

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.

arXiv:cond-mat/0208566Physical Review LettersDec 9, 200212 citations

Towards a field theory of spin glasses

Imre Kondor

Advances in Solid State PhysicsSep 11, 20070 citations

d=6

scaling is restored. Below

d=6

all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.