One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

Monthus, Cécile

doi:10.1088/1742-5468/2014/14/p06015

Cited by 13 publications

(27 citation statements)

References 117 publications

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“…This rules coincides with the zero-temperature RG studied in detail in [40] and its growth is governed by the droplet exponent θ = 1 − σ of Eq. 81 as it should (see [40] for more details)…”

Section: Bsupporting

confidence: 86%

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Real-space renormalization for the finite temperature statics and dynamics of the Dyson long-ranged ferromagnetic and spin-glass models

Monthus¹

2016

J. Stat. Mech.

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The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving Long-Ranged coupling J(r) ∝ r −1−σ in the region 1/2 < σ < 1 where there exists a non-mean-field-like thermal Ferromagnetic-Paramagnetic transition, the RG flows are explicitly solved: the characteristic relaxation time τ (L) follows the critical power-law τ (L) ∝ L zc (σ) at the phase transition and the activated law ln τ (L) ∝ L ψ with ψ = 1 − σ in the ferromagnetic phase. For the Spin-Glass model involving random Long-Ranged couplings of variance J 2 (r) ∝ r −2σ in the region 2/3 < σ < 1 where there exists a non-mean-field-like thermal SpinGlass-Paramagnetic transition, the coupled RG flows of the couplings and of the relaxation times are studied numerically : the relaxation time τ (L) follows some power-law τ (L) ∝ L zc(σ) at criticality and the activated law ln τ (L) ∝ L ψ in the Spin-Glass phase with the dynamical exponent ψ = 1 − σ = θ coinciding with the droplet exponent governing the flow of the couplings J(L) ∝ L θ .

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Section: Bsupporting

confidence: 86%

“…This suggests that at finite temperature T , it is not possible to write consistent closed renormalization rules for the couplings alone, in contrast to the zero temperature limit where it is possible [40].…”

Section: Discussionmentioning

confidence: 99%

Real-space renormalization for the finite temperature statics and dynamics of the Dyson long-ranged ferromagnetic and spin-glass models

Monthus¹

2016

J. Stat. Mech.

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“…This rule coincides with the RG rule for the classical spin-glass at zero temperature studied in detail in [19,20], and in particular, the variance evolves according to…”

Section: F Rg Flows Deep In the Spin-glass Phasesupporting

confidence: 80%

Dyson hierarchical long-ranged quantum spin-glass via real-space renormalization

Monthus¹

2015

J. Stat. Mech.

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We consider the Dyson hierarchical version of the quantum Spin-Glass with random Gaussian couplings characterized by the power-law decaying variance J 2 (r) ∝ r −2σ and a uniform transverse field h. The ground state is studied via real-space renormalization to characterize the spinglassparamagnetic zero temperature quantum phase transition as a function of the control parameter h. In the spinglass phase h < hc, the typical renormalized coupling grows with the length scale L as the power-law J typ L (h) ∝ Υ(h)L θ with the classical droplet exponent θ = 1 − σ, where the stiffness modulus vanishes at criticality Υ(h) ∝ (hc − h) µ , whereas the typical renormalized transverse field decays exponentially h typ L (h) ∝ e − L ξ in terms of the diverging correlation length ξ ∝ (hc − h) −ν . At the critical point h = hc, the typical renormalized coupling J typ L (hc) and the typical renormalized transverse field h typ L (hc) display the same power-law behavior L −z with a finite dynamical exponent z. The RG rules are applied numerically to chains containing L = 2 12 = 4096 spins in order to measure these critical exponents for various values of σ in the region 1/2 < σ < 1.I.

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“…Equilibrium properties of random systems SDRG has been also used to analyze the equilibrium phase transitions of various classical systems, as reviewed in [3], while more recent applications include the randomly layered Heisenberg magnet [278], the wetting transition on the Cayley tree [279], the DNA denaturation transition [280]. In the field of classical spin-glasses, some SDRG procedure have been also introduced to study the spin-glass phase of the Long-Ranged Spin-Glass chain [281] or the fractal dimension of interfaces in Short-Ranged Spin-Glasses as a function of the dimension d [282][283][284].…”

Section: Other Classical Modelsmentioning

confidence: 99%

Strong disorder RG approach – a short review of recent developments

Iglói

Monthus

2018

Eur. Phys. J. B

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Relations between SDRG and Entanglement-Algorithms 10 VI. Localized and Many-Body-Localized Phases of quantum spin chains 11 A. RSRG-X for excited eigenstates 11 B. RSRG-t for the unitary dynamics 11 C. Non-equilibrium dynamical scaling of observables 12 D. Comparison with other RG procedures existing in the field of Many-Body-Localization 13 VII. Floquet dynamics of periodically driven chains in their localized phases 13 VIII. Open dissipative quantum spin chains 13 A. Quantum spin chains coupled to a bath of quantum oscillators 13 B. Lindblad dynamics for random quantum spin chains 14 IX. Anderson localization models 14 X. Random contact process 14 A. Strong disorder RG rules 15 B. Long range spreading 15 C. Temporal disorder 15 XI. Classical master equations 16 A. Real-space renormalization for random walks in random media 16 B. RG in configuration-space for the dynamics of classical many-body models 16 XII. Random classical oscillators 17 A. Random elastic networks 17 B. Synchronisation of interacting non-linear dissipative classical oscillators 17 XIII. Other classical models 17 A. Equilibrium properties of random systems 17 B. Extremes of stochastic processes 18 XIV. Conclusion 18

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One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

Cited by 13 publications

References 117 publications

Real-space renormalization for the finite temperature statics and dynamics of the Dyson long-ranged ferromagnetic and spin-glass models

Real-space renormalization for the finite temperature statics and dynamics of the Dyson long-ranged ferromagnetic and spin-glass models

Dyson hierarchical long-ranged quantum spin-glass via real-space renormalization

Strong disorder RG approach – a short review of recent developments

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