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Europhysics Letters (EPL)

Damage spreading and ferromagnetic order in the three-dimensional ±J Edwards-Anderson spin glass model

M. Leticia Rubio Puzzo, FEDERICO J. ROMÁ, S. Bustingorry, Pablo M. Gleiser

Published Aug 1, 2010• 5 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/91/37008

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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.
Griffiths-like phase in the three-dimensional ±J\pm J±J Edwards-Anderson spin-glass model
Using information of the ground state topology and the damage spreading technique we show a Griffiths-like phase is present in the three-dimensional ±J\pm J±J Edwards-Anderson spin glass model. With spin-flipping dynamics damage spreads for temperatures larger than TgT_{\mathrm{g}}Tg​, the glass transition temperature. With spin-orienting dynamics and for temperatures in Tg<T<TdT_{\mathrm{g}} < T < T_{\mathrm{d}}Tg​<T<Td​, damage spreads over a finite region of the system, composed of finite clusters of ferromagnetic character. TdT_{\mathrm{d}}Td​ is the spin-orienting damage critical temperature, which is of the same order as the critical temperature of the ferromagnetic Ising model, TcT_{\mathrm{c}}Tc​. The present results allow us to identify the clusters which originate the Griffiths-like phase in the present model.
We present results showing the correlation between the out-of-equilibrium dynamics and the equilibrium damage-spreading process in the two-dimensional ± J Edwards–Anderson model at low temperatures. A key ingredient in our analysis is the projection of finite temperature spin configurations onto the ground state topology of the system. In particular, through numerical simulations we correlate ground state information with the out-of-equilibrium dynamics. We also analyse how the propagation of a small perturbation in equilibrated systems is related to the ground state topology. This damage-spreading study unveils the presence of rigid clusters of spins. We claim that these clusters give rise to the slow out-of-equilibrium dynamics observed in the temperature range between the glass temperature T g = 0 of the two-dimensional ± J Edwards–Anderson model and the critical temperature T c of the pure ferromagnetic Ising model.
We investigate the ferromagnetic-glassy transitions that separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider the cubic-lattice $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model with bond distribution $P(J)=p\ensuremath{\delta}(J\ensuremath{-}1)+(1\ensuremath{-}p)\ensuremath{\delta}(J+1)$, and present a numerical Monte Carlo study of the critical behavior along the line that marks the onset of ferromagnetism. The finite-size scaling analysis of the Monte Carlo data shows that the ferromagnetic-glassy transition line is slightly reentrant. As a consequence, for an interval of the disorder parameter ppp, around $p\ensuremath{\approx}0.77$, the system presents a low-temperature glassy phase, an intermediate ferromagnetic phase, and a high-temperature paramagnetic phase. Along the ferromagnetic-glassy transition line, magnetic correlations show a universal critical behavior with critical exponents $\ensuremath{\nu}=0.96(2)$ and $\ensuremath{\eta}=\ensuremath{-}0.39(2)$. The hyperscaling relation $\ensuremath{\beta}/\ensuremath{\nu}=(1+\ensuremath{\eta})/2$ is satisfied at the transitions, so that $\ensuremath{\beta}/\ensuremath{\nu}=0.305(10)$. This magnetic critical behavior represents a new universality class for ferromagnetic transitions in Ising-type disordered systems. Overlap correlations are apparently not critical and show a smooth behavior across the transition.
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.
The nature of the freezing process in two- and three-dimensional Ising spin glasses with bonds J ij =+or-J has been investigated. Monte Carlo simulations indicate that the characteristic cusp in the susceptibility chi is a non-equilibrium phenomenon resulting from the finite observation times available for the computation of chi (or its experimental measurement). This picture of the freezing process, which is illustrated by explicit calculation for the one-dimensional Ising spin glass, implies chi =1/k B T for all temperatures, or that the Edwards-Anderson order parameter q vanishes. Investigation of the ground states of certain periodic models in two and three dimensions show that every spin belongs to a finite cluster which may be turned over with no cost of energy, so that q is rigorously zero for such models. It is argued that this result holds also for the fully random models.