Spin glasses in a field: Three and four dimensions as seen from one space dimension
arXiv:1211.7297 · doi:10.1103/PhysRevB.87.024414
Abstract
We study the existence of a line of transitions of an Ising spin glass in a magnetic field-known as the de Almeida-Thouless line-using one-dimensional power-law diluted Ising spin-glass models. We choose the power-law exponent to have values that approximately correspond to three- and four-dimensional nearest-neighbor systems and perform a detailed finite-size scaling analysis of the data for large linear system sizes, both using a new approach proposed recently [Phys. Rev. Lett. 103, 267201 (2009)], as well as traditional approaches. Our results for the model corresponding to a three-dimensional system are consistent with there being no de Almeida-Thouless line, although the new finite-size scaling approach does not rule one out. For the model corresponding to four space dimensions, the new and traditional finite-size scaling analyses give conflicting results, indicating the need for a better understanding of finite-size scaling of spin glasses in a magnetic field.
10 pages, 8 figures, loads of fun!
References in corpus (25)
- Exchange Monte Carlo Method and Application to Spin Glass Simulations
- Critical Behavior of the Three-Dimensional Ising Spin Glass
- Universality in three-dimensional Ising spin glasses: A Monte Carlo study
- Universal Finite Size Scaling Functions in the 3D Ising Spin Glass
- Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
- Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
- 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
- Behavior of Ising Spin Glasses in a Magnetic Field
- Thermodynamic glass transition in a spin glass without time-reversal symmetry
- The correspondence between long-range and short-range spin glasses
- The critical behavior of 3D Ising glass models: universality and scaling corrections
- Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions
- Ising Spin Glasses in a Magnetic Field
- Zero-temperature responses of a 3D spin glass in a field
- Instability of the mean-field states and generalization of phase separation in long-range interacting systems
- Field-Shift Aging Protocol on the 3D Ising Spin-Glass Model: Dynamical Crossover between the Spin-Glass and Paramagnetic States
- Magnetic field chaos in the SK Model
- Critical Behavior of the 4D Spin Glass in Magnetic Field
- Correlations between the dynamics of parallel tempering and the free-energy landscape in spin glasses
- Universality and universal finite-size scaling functions in four-dimensional Ising spin glasses
- Spin glasses in the non-extensive regime
- Spin glasses and algorithm benchmarks: A one-dimensional view
- Bond diluted Levy spin-glass model and a new finite size scaling method to determine a phase transition
Cited by in corpus (41)
- Growing timescales and lengthscales characterizing vibrations of amorphous solids
- Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
- Absence of Marginal Stability in a Structural Glass
- The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
- Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
- Maximum-Entropy Inference with a Programmable Annealer
- Finding spin-glass ground states using quantum walks
- Dynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field
- What can spin glass theory and analogies tell us about ferroic glasses?
- Competing interaction in magnets: the root of ordered disorder or only frustration?
- Hierarchical landscape of hard disk glasses
- Low-temperature anomalies of a vapor deposited glass
- From local to global ground states in Ising spin glasses
- Finite size corrections to disordered Ising models on Random Regular Graphs
- Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
- Parallel Tempering Simulation of the three-dimensional Edwards-Anderson Model with Compact Asynchronous Multispin Coding on GPU
- One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses
- Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature
- Finite-size critical scaling in Ising spin glasses in the mean-field regime
- The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
- Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem
- Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
- Spin-glass dynamics in the presence of a magnetic field: exploration of microscopic properties
- Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices
- Novel disordering mechanism in ferromagnetic systems with competing interactions
- Dynamic scaling analysis of the long-range RKKY Ising spin glass DyYRuSi
- Critical Point Scaling of Ising Spin Glasses in a Magnetic Field
- Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models
- Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin-glass
- Exact ground states of one-dimensional long-range random-field Ising magnets
- Numerical test of the replica-symmetric Hamiltonian for the correlations of the critical state of spin glasses in a field
- de Almeida-Thouless instability in short-range Ising spin-glasses
- Learning to find order in disorder
- Chaos properties of the one-dimensional long-range Ising spin-glass
- Physical observables of the Ising spin glass in 6-epsilon dimensions: asymptotical behavior around the critical fixed point
- 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)
- Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: above and below the upper critical range
- One-loop topological expansion for spin glasses in the large connectivity limit
- Precursors of the Spin Glass Transition in Three Dimensions
- Charge avalanches and depinning in the Coulomb glass: The role of long-range interactions
- Boolean decision problems with competing interactions on scale-free networks: Equilibrium and nonequilibrium behavior in an external bias