Local excitations in mean field spin glasses

Abstract

We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like graphs, equivalent to a replica symmetric computation, and then directly on finite connectivity random lattices. In the first model, characterized by a discontinuous replica symmetry breaking, we found that the energy of finite volume excitation is infinite whereas in the dilute mean field model, described by a continuous replica symmetry breaking, it slowly decreases with sizes and saturates at a finite value, in contrast with what would be naively expected. The geometrical properties of these excitations are similar to those of lattice animals or branched polymers. We discuss the meaning of these results in terms of replica symmetry breaking and also possible relevance in finite dimensional systems.

7 pages, 4 figures, accepted for publication

References in corpus (17)

• The Bethe lattice spin glass revisited
• Nature of the Spin Glass State
• Spin and link overlaps in 3-dimensional spin glasses
• Energy exponents and corrections to scaling in Ising spin glasses
• Renormalization for Discrete Optimization
• On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses
• Interface energies in Ising spin glasses
• Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass
• Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses
• Large-scale low-energy excitations in 3-d spin glasses
• A geometrical picture for finite dimensional spin glasses
• A hierarchical approach for computing spin glass ground states
• Near optimal configurations in mean field disordered systems
• Non-compact local excitations in spin glasses
• Replica field theory and renormalization group for the Ising spin glass in an external magnetic field
• Local excitations of a spin glass in a magnetic field
• Scaling and infrared divergences in the replica field theory of the Ising spin glass

Cited by in corpus (3)

• Disorder chaos in spin glasses
• Statistics of low energy excitations for the directed polymer in a $1+d$ random medium ($d=1,2,3$)
• A Relation between Disorder Chaos and Incongruent States in Spin Glasses on ${\mathbb{Z}}^d$