Spin-glass behaviour on random lattices

Abstract

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that $w=1/2$, correponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase ($w<1/2$) from a region with spin-glass, ferromagnetic, mixed, and paramagnetic phases ($w>1/2$).

References in corpus (16)

• Critical phenomena in complex networks
• Spin-Glass Theory for Pedestrians
• Phase Transitions in the Coloring of Random Graphs
• The critical behavior of three-dimensional Ising spin glass models
• Behavior of Ising Spin Glasses in a Magnetic Field
• Elusive Glassy Phase in the Random Field Ising Model
• Finite-Connectivity Spin-Glass Phase Diagrams and Low Density Parity Check Codes
• Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations
• No spin glass phase in ferromagnetic random-field random-temperature scalar Ginzburg-Landau model
• Near optimal configurations in mean field disordered systems
• Antiferromagnetic Ising model in small-world networks
• Spin glass behavior of the antiferromagnetic Ising model on a scale-free network
• Replica symmetry breaking in the `small world' spin glass
• Antiferromagnetic Ising model in scale-free networks
• Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
• Zero temperature phase diagram of finite connectivity spin glasses

Cited by in corpus (1)

• Spin-glass transition in the Ising model on multiplex networks