Chaos properties of the one-dimensional long-range Ising spin-glass

Abstract

For the long-range one-dimensional Ising spin-glass with random couplings decaying as $J(r)\propto r^{-\sigma }$, the scaling of the effective coupling defined as the difference between the free-energies corresponding to Periodic and Antiperiodic boundary conditions $J^R(N)\equiv F^{(P)}(N)-F^{(AP)}(N)\sim N^{\theta (\sigma )}$ defines the droplet exponent $\theta (\sigma )$. Here we study numerically the instability of the renormalization flow of the effective coupling $J^R(N)$ with respect to magnetic, disorder and temperature perturbations respectively, in order to extract the corresponding chaos exponents ${\zeta }_H(\sigma )$, ${\zeta }_J(\sigma )$ and ${\zeta }_T(\sigma )$ as a function of $\sigma$. Our results for ${\zeta }_T(\sigma )$ are interpreted in terms of the entropy exponent ${\theta }_S(\sigma )\simeq 1/3$ which governs the scaling of the entropy difference $S^{(P)}(N)-S^{(AP)}(N)\sim N^{{\theta }_S(\sigma )}$. We also study the instability of the ground state configuration with respect to perturbations, as measured by the spin overlap between the unperturbed and the perturbed ground states, in order to extract the corresponding chaos exponents ${\zeta }_H^{overlap}(\sigma )$ and ${\zeta }_J^{overlap}(\sigma )$.

14 pages, 15 figures

References in corpus (22)

• 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
• Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses
• Spin glasses in a field: Three and four dimensions as seen from one space dimension
• Zero and low temperature behavior of the two-dimensional $\pm J$ Ising spin glass
• The correspondence between long-range and short-range spin glasses
• Universality-class dependence of energy distributions in spin glasses
• Disorder chaos in spin glasses
• Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
• Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions
• Probing tails of energy distributions using importance-sampling in the disorder with a guiding function
• Ultrametricity and clustering of states in spin glasses: A one-dimensional view
• Scaling Analysis of Domain-Wall Free-Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field
• Temperature Chaos in Two-Dimensional Ising Spin Glasses with Binary Couplings: a Further Case for Universality
• On temperature chaos in Ising and XY Spin Glasses
• Spin glasses and algorithm benchmarks: A one-dimensional view
• Bond chaos in the Sherrington-Kirkpatrick model
• Ultrametric probe of the spin-glass state in a field
• An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
• Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $\psi =d_s/2$ for the barrier exponent
• Chaotic Spin Correlations in Frustrated Ising Hierarchical Lattices

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