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Journal de Physique I

Damage Spreading in ±J Asymmetric Ising Spin Glasses

Rita M. C. de Almeida, L. Bernadi, Ian A. Campbell

Published Mar 1, 1995• 3 citations
Publisher

Abstract

Spin glasses in dimensions 2, 3, 4 and mean field are studied numerically as a function of the degree of asymmetry of the interactions between spins. Damage spreading data are used to assess the effects on the spin glass ordering of introducing asymmetry in the couplings. In all dimensions the critical temperature for damage spreading is rather insensitive to the asymmetry, but the spin glass ordering is strongly suppressed by any finite degree of asymmetry. We discuss the physical significance of the damage spreading parameter.

DOI
10.1051/jp1:1995106

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The dynamical critical behaviour of the ± J spin glass at the damage-spreading threshold

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The dynamical critical behaviour of the ± J Ising spin glass is investigated at the damage-spreading threshold T d . The dynamical critical exponent z is observed as z = 1.75 ± 0.08 at T d = 1.70 for d = 2 and z = 1.73 ± 0.14 at T d = 3.92 for d = 3. The fractal dimensions of the damage cluster are estimated as d f = 1.35 ± 0.08 for the 2D Ising spin glass and d f = 1.47 ± 0.08 for the 3D system, which satisfy the equation d f = d − β/ν within the error bar.

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Damage spreading in the Ising model with a microcanonical constraint

F. G. Brady Moreira, Adauto J. F. de Souza, Ananias M. Mariz

We study damage spreading in the ferromagnetic Ising model, on the square lattice, by performing numerical simulations in the microcanonical ensemble. Although the damage spreads for all temperature values, a dynamical critical phenomenon is observed at ${\mathit{T}}_{\mathit{d}}$=1.020(2)${\mathit{T}}_{\mathit{C}}$ (${\mathit{T}}_{\mathit{C}}$ is the Curie temperature): For T\ensuremath{\ge}${\mathit{T}}_{\mathit{d}}$ the damage D(t) is insensitive to its initial value D(0), while for T${\mathit{T}}_{\mathit{d}}$ a weak dependence on D(0) is present in such a way that for each T there are two values of D(t) corresponding to the initial conditions D(0)1/2 and D(0)>1/2. We have also identified a convenient order parameter to characterize the transition occurring at ${\mathit{T}}_{\mathit{d}}$. \textcopyright{} 1996 The American Physical Society.

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Spin-1 Ising model: Exact damage-spreading relations and numerical simulations

Aécia S. D. dos Anjos, Ananias M. Mariz, Fernando Dantas Nobre +1 more

The nearest-neighbor-interaction spin-1 Ising model is investigated within the damage-spreading approach. Exact relations involving quantities computable through damage-spreading simulations and thermodynamic properties are derived for such a model, defined in terms of a very general Hamiltonian that covers several spin-1 models of interest in the literature. Such relations presuppose translational invariance and hold for any ergodic dynamical procedure, leading to an efficient tool for obtaining thermodynamic properties. The implementation of the method is illustrated through damage-spreading simulations for the ferromagnetic spin-1 Ising model on a square lattice. The two-spin correlation function and the magnetization are obtained, with precise estimates of their associated critical exponents and of the critical temperature of the model, in spite of the small lattice sizes considered. These results are in good agreement with the universality hypothesis, with critical exponents in the same universality class of the spin- 12 Ising model. The advantage of the present method is shown through a significant reduction of finite-size effects by comparing its results with those obtained from standard Monte Carlo simulations.

Physical Review E•Sep 3, 2008•1 citation
Spin glasses in dimensions 2, 3, 4 and mean field are studied numerically as a function of the degree of asymmetry of the interactions between spins. Damage spreading data are used to assess the effects on the spin glass ordering of introducing asymmetry in the couplings. In all dimensions the critical temperature for damage spreading is rather insensitive to the asymmetry, but the spin glass ordering is strongly suppressed by any finite degree of asymmetry. We discuss the physical significance of the damage spreading parameter.
Using information of the ground-state topology we show that the damage spreading technique unveils ferromagnetic order in the three-dimensional ± J Edwards-Anderson spin glass model. With spin-flipping dynamics damage spreads for temperatures larger than T g , the glass transition temperature. With spin-orienting dynamics and for temperatures in T g < T < T d , damage spreads over a finite region of the system, composed of finite clusters of ferromagnetic character. T d is the spin-orienting damage critical temperature, which is of the same order as the critical temperature of the ferromagnetic Ising model, T c . The present results allow for an interpretation within a single framework of known —and sometimes puzzling— results, giving an intuitive picture for growing order in spin glasses.
We study damage spreading in the ferromagnetic Ising model, on the square lattice, by performing numerical simulations in the microcanonical ensemble. Although the damage spreads for all temperature values, a dynamical critical phenomenon is observed at Td{\mathit{T}}_{\mathit{d}}Td​=1.020(2)TC{\mathit{T}}_{\mathit{C}}TC​ (TC{\mathit{T}}_{\mathit{C}}TC​ is the Curie temperature): For T\ensuremath{\ge}Td{\mathit{T}}_{\mathit{d}}Td​ the damage D(t) is insensitive to its initial value D(0), while for TTd{\mathit{T}}_{\mathit{d}}Td​ a weak dependence on D(0) is present in such a way that for each T there are two values of D(t) corresponding to the initial conditions D(0)1/2 and D(0)>1/2. We have also identified a convenient order parameter to characterize the transition occurring at Td{\mathit{T}}_{\mathit{d}}Td​. \textcopyright{} 1996 The American Physical Society.
The nearest-neighbor-interaction spin-1 Ising model is investigated within the damage-spreading approach. Exact relations involving quantities computable through damage-spreading simulations and thermodynamic properties are derived for such a model, defined in terms of a very general Hamiltonian that covers several spin-1 models of interest in the literature. Such relations presuppose translational invariance and hold for any ergodic dynamical procedure, leading to an efficient tool for obtaining thermodynamic properties. The implementation of the method is illustrated through damage-spreading simulations for the ferromagnetic spin-1 Ising model on a square lattice. The two-spin correlation function and the magnetization are obtained, with precise estimates of their associated critical exponents and of the critical temperature of the model, in spite of the small lattice sizes considered. These results are in good agreement with the universality hypothesis, with critical exponents in the same universality class of the spin- 12 Ising model. The advantage of the present method is shown through a significant reduction of finite-size effects by comparing its results with those obtained from standard Monte Carlo simulations.