Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Modern Physics

Out-of-Equilibrium Dissipative ac—Susceptibility in Quantum Ising Spin Glass

Gaetano Busiello

Published Jan 1, 2013• 2 citations
Publisher

Abstract

The imaginary part of the non-equilibrium magnetic susceptibility of Ising spin glass in a transverse field under time-dependent longitudinal external magnetic field has been calculated at very low temperature on the basis of quantum droplet model and quantum linear response theory. Quantum and aging effects on the low temperature dynamics of the model are discussed. A comparison with recent theoretical and experimental data in spin glass is made.

DOI
10.4236/jmp.2013.46108

Related papers

Nonequilibrium dynamics of quantum spin glass in an AC magnetic field

Gaetano Busiello, R. V. Saburova, V. G. Sushkova +1 more

The ageing effect is studied analytically in a disordered quantum system interacting with its surroundings and subjected to an external ac magnetic field. Energy dissipation is due to the interaction of the system with a set of independent harmonic oscillators, imitating a quantum thermal bath. Dynamic equations for the autocorrelation function and linear-response function are derived using the method of closed-path integrals. The effect of an external field is studied on the correlation function and response in the spin-glass and paramagnetic phases. Both functions are found to depend on the spin interaction strength.

Physics of the Solid State•Feb 1, 2004•4 citations

Aging in two-dimensional Ising spin glasses

A. G. Schins, E. M. Dons, A. F. M. Arts +4 more

Aging of two-dimensional (2D) Ising spin glasses with short-range interactions ${\mathrm{Rb}}_{2}$${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$${\mathrm{F}}_{4}$ (${\mathit{T}}_{\mathit{c}}$=0) is studied in the critical regime via the low-frequency ac susceptibility and via the dc magnetization for x=0.22 and 0.33. After quenching to low temperatures, slow logarithmic relaxation is observed for both the in-phase and out-of-phase ac susceptibilities. Using the droplet scaling model, the spin-glass correlation length R is concluded to increase after a temperature quench as R\ensuremath{\propto}(lnt${)}^{1/\mathrm{\ensuremath{\psi}}}$, with t in units of some microscopic time. The exponent \ensuremath{\psi}=1.0\ifmmode\pm\else\textpm\fi{}0.1 compares with recent theoretical results and numerical simulations for 2D short-range Ising spin glasses. The waiting-time dependence found for the field-cooled and zero-field-cooled dc magnetizations points to a markedly slower crossover from the quasiequilibrium to the nonequilibrium regime than in 3D. From experiments with different cooling histories, finally, the equilibrium spin-glass state is inferred to be strongly dependent on the temperature.

Physical review. B, Condensed matter•Dec 1, 1993•18 citations

Aging effects in the nonequilibrium quantum spin glass in weak magnetic fields

G. Buziello, E. V. Gazeeva, R. V. Saburova +2 more

This work is devoted to a theoretical study of effects of aging in a disordered quantum system being in contact with an interior surroundings and subject to the influence of external alternating fields. The dissipation is realized via coupling with a set of independent harmonic oscillators, which imitate a quantum thermostat (bath), and with an external field. Using the formalism of closed-path integrals, dynamic equations are derived for the autocorrelation and linear-response functions. The dependences of correlation, response, and integrated-response functions on temperature, waiting time, and quantum parameter are studied. The effect of external fields on the behavior of these functions is analyzed. A qualitative agreement with experimental data have been found.

The Physics of Metals and Metallography•Sep 1, 2006•1 citation

ON THE NONLINEAR SUSCEPTIBILITY OF THE QUANTUM ISING SPIN GLASS MODEL IN A RANDOM FIELD

Gaetano Busiello, R. V. Saburova

We calculate the static bulk nonlinear susceptibility for Ising spin glass model with pairwise interactions, in a transverse field and longitudinal random field. Paramagnetic-spin glass transition is considered and connections with previous theoretical and experimental results are made.

Modern Physics Letters B•Nov 10, 1996•4 citations

Model calculation for the susceptibility of a quantum spin glass

Varsha Banerjee, Sushanta Dattagupta

We have studied the dynamic susceptibility in a quantum spin glass which is described by an Ising model in a transverse field, the latter introducing quantum tunneling in an otherwise classical problem. An effective single-spin Hamiltonian is obtained on the basis of an extant thermofield dynamic approach. The coupling to a dissipative heat bath is designed to affect thermal as well as quantal fluctuations and to yield Glauber kinetics in the absence of the transverse field. A resolvent expansion of the underlying time-development operator is then set up and the dynamic susceptibility calculated to leading order in perturbation theory. It is shown that the frequency of the peak of the susceptibility shifts towards higher values of \ensuremath{\omega}, its amplitude is reduced and peaks are broadened as quantum effects strengthen. Our results are in qualitative agreement with the experimentally studied crystal-field-split system of ${\mathrm{LiHo}}_{\mathit{x}}$${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{F}}_{4}$ by Wu et al.

Physical review. B, Condensed matter•Oct 1, 1994•9 citations

Non-Equilibrium Dynamics and Aging in the Three-Dimensional Ising Spin-Glass Model

Heiko Rieger

The low temperature dynamics of the three dimensional Ising spin glass in zero field with a discrete bond distribution is investigated via MC simulations. The thermoremanent magnetization is found to decay algebraically and the temperature dependent exponents agree very well with the experimentally determined values. The nonequilibrium autocorrelation function C(t,tw) shows a crossover at the waiting (or aging) time tw from algebraic quasi-equilibrium decay for times t≪tw to another, faster algebraic decay for t≫tw with an exponent similar to one for the remanent magnetization.

•Jan 1, 1993•101 citations
The imaginary part of the non-equilibrium magnetic susceptibility of Ising spin glass in a transverse field under time-dependent longitudinal external magnetic field has been calculated at very low temperature on the basis of quantum droplet model and quantum linear response theory. Quantum and aging effects on the low temperature dynamics of the model are discussed. A comparison with recent theoretical and experimental data in spin glass is made.
The ageing effect is studied analytically in a disordered quantum system interacting with its surroundings and subjected to an external ac magnetic field. Energy dissipation is due to the interaction of the system with a set of independent harmonic oscillators, imitating a quantum thermal bath. Dynamic equations for the autocorrelation function and linear-response function are derived using the method of closed-path integrals. The effect of an external field is studied on the correlation function and response in the spin-glass and paramagnetic phases. Both functions are found to depend on the spin interaction strength.
Aging of two-dimensional (2D) Ising spin glasses with short-range interactions Rb2{\mathrm{Rb}}_{2}Rb2​${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Cox{\mathrm{Co}}_{\mathit{x}}Cox​F4{\mathrm{F}}_{4}F4​ (Tc{\mathit{T}}_{\mathit{c}}Tc​=0) is studied in the critical regime via the low-frequency ac susceptibility and via the dc magnetization for x=0.22 and 0.33. After quenching to low temperatures, slow logarithmic relaxation is observed for both the in-phase and out-of-phase ac susceptibilities. Using the droplet scaling model, the spin-glass correlation length R is concluded to increase after a temperature quench as R\ensuremath{\propto}(lnt${)}^{1/\mathrm{\ensuremath{\psi}}}$, with t in units of some microscopic time. The exponent \ensuremath{\psi}=1.0\ifmmode\pm\else\textpm\fi{}0.1 compares with recent theoretical results and numerical simulations for 2D short-range Ising spin glasses. The waiting-time dependence found for the field-cooled and zero-field-cooled dc magnetizations points to a markedly slower crossover from the quasiequilibrium to the nonequilibrium regime than in 3D. From experiments with different cooling histories, finally, the equilibrium spin-glass state is inferred to be strongly dependent on the temperature.
This work is devoted to a theoretical study of effects of aging in a disordered quantum system being in contact with an interior surroundings and subject to the influence of external alternating fields. The dissipation is realized via coupling with a set of independent harmonic oscillators, which imitate a quantum thermostat (bath), and with an external field. Using the formalism of closed-path integrals, dynamic equations are derived for the autocorrelation and linear-response functions. The dependences of correlation, response, and integrated-response functions on temperature, waiting time, and quantum parameter are studied. The effect of external fields on the behavior of these functions is analyzed. A qualitative agreement with experimental data have been found.
We have studied the dynamic susceptibility in a quantum spin glass which is described by an Ising model in a transverse field, the latter introducing quantum tunneling in an otherwise classical problem. An effective single-spin Hamiltonian is obtained on the basis of an extant thermofield dynamic approach. The coupling to a dissipative heat bath is designed to affect thermal as well as quantal fluctuations and to yield Glauber kinetics in the absence of the transverse field. A resolvent expansion of the underlying time-development operator is then set up and the dynamic susceptibility calculated to leading order in perturbation theory. It is shown that the frequency of the peak of the susceptibility shifts towards higher values of \ensuremath{\omega}, its amplitude is reduced and peaks are broadened as quantum effects strengthen. Our results are in qualitative agreement with the experimentally studied crystal-field-split system of LiHox{\mathrm{LiHo}}_{\mathit{x}}LiHox​${\mathrm{Y}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$F4{\mathrm{F}}_{4}F4​ by Wu et al.
The low temperature dynamics of the three dimensional Ising spin glass in zero field with a discrete bond distribution is investigated via MC simulations. The thermoremanent magnetization is found to decay algebraically and the temperature dependent exponents agree very well with the experimentally determined values. The nonequilibrium autocorrelation function C(t,tw) shows a crossover at the waiting (or aging) time tw from algebraic quasi-equilibrium decay for times t≪tw to another, faster algebraic decay for t≫tw with an exponent similar to one for the remanent magnetization.