Skip to Main content Skip to Navigation
Journal articles

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) ∝ r −σ , the scaling of the effective coupling defined as the difference between the free-energies corresponding to Periodic and Antiperiodic boundary conditions J R (N) ≡ F (P) (N) − F (AP) (N) ∼ N θ(σ) defines the droplet exponent θ(σ). 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 ζH(σ), ζJ (σ) and ζT (σ) as a function of σ. Our results for ζT (σ) are interpreted in terms of the entropy exponent θS(σ) ≃ 1/3 which governs the scaling of the entropy difference S (P) (N) − S (AP) (N) ∼ N θ S (σ). 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 ζoverlapH (σ) and ζoverlapJ (σ).
Document type :
Journal articles
Complete list of metadatas

Cited literature [62 references]  Display  Hide  Download

https://hal-cea.archives-ouvertes.fr/cea-01323269
Contributor : Emmanuelle de Laborderie <>
Submitted on : Monday, May 30, 2016 - 12:21:51 PM
Last modification on : Monday, February 10, 2020 - 6:13:40 PM
Long-term archiving on: : Wednesday, August 31, 2016 - 10:22:20 AM

File

1310.2815v1.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Cécile Monthus, Thomas Garel. Chaos properties of the one-dimensional long-range Ising spin-glass. Journal of Statistical Mechanics, 2014, 2014 (3), pp.20. ⟨10.1088/1742-5468/2014/03/P03020⟩. ⟨cea-01323269⟩

Share

Metrics

Record views

144

Files downloads

221