Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions

Abstract

Ising spin-glass systems with long-range interactions ($J(r)\sim r^{-\sigma }$) are considered. A numerical study of the critical behaviour is presented in the non-mean-field region together with an analysis of the probability distribution of the overlaps and of the ultrametric structure of the space of the equilibrium configurations in the frozen phase. Also in presence of diverging thermodynamical fluctuations at the critical point the behaviour of the model is shown to be of the Replica Simmetry Breaking type and there are hints of a non-trivial ultrametric structure. The parallel tempering algorithm has been used to simulate the dynamical approach to equilibrium of such systems.

15 pages and 12 figures

References in corpus (2)

• Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
• Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses

Cited by in corpus (21)

• Diluted one-dimensional spin glasses with power law decaying interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Ising spin glass transition in magnetic field out of mean-field
• Universality-class dependence of energy distributions in spin glasses
• One dimensional phase-ordering in the Ising model with space decaying interactions
• Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions
• Overlap Interfaces in Hierarchical Spin-Glass models
• Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field
• Non-perturbative effects in spin glasses
• The ordered phase of the one-dimensional Ising spin glass with long-range interactions
• One-dimensional infinite component vector spin glass with long-range interactions
• Bond diluted Levy spin-glass model and a new finite size scaling method to determine a phase transition
• Dynamic scaling analysis of the long-range RKKY Ising spin glass Dy${}_x$Y${}_{1-x}$Ru${}_2$Si${}_2$
• Exact ground states of one-dimensional long-range random-field Ising magnets
• Ultrametric Fitting by Gradient Descent
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
• 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)
• Ordering of the Heisenberg spin glass in four dimensions
• Identification of the critical temperature from non-equilibrium time-dependent quantities
• Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions