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Europhysics Letters (EPL)

The Ising Spin Glass and Phase Space Geometry

Ian A. Campbell, L. de Arcangelis

Published Dec 1, 1990• 15 citations
Publisher

Abstract

Through “damage spreading” numerical simulations, we study the Ising spin glass in three dimensions with ± J near-neighbour interactions. The results are compared to other simulation data; we conclude that the damage spreading method can provide good estimates of the transition temperatures in this type of system. A discussion is given of phase transitions in spin glasses in terms of the geometry of phase space.

DOI
10.1209/0295-5075/13/7/003

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Using information of the ground state topology and the damage spreading technique we show a Griffiths-like phase is present in the three-dimensional $\pm J$ Edwards-Anderson spin glass model. With spin-flipping dynamics damage spreads for temperatures larger than $T_{\mathrm{g}}$, the glass transition temperature. With spin-orienting dynamics and for temperatures in $T_{\mathrm{g}} < T < T_{\mathrm{d}}$, damage spreads over a finite region of the system, composed of finite clusters of ferromagnetic character. $T_{\mathrm{d}}$ is the spin-orienting damage critical temperature, which is of the same order as the critical temperature of the ferromagnetic Ising model, $T_{\mathrm{c}}$. The present results allow us to identify the clusters which originate the Griffiths-like phase in the present model.

arXiv:0911.4837•Nov 25, 2009•0 citations
Through “damage spreading” numerical simulations, we study the Ising spin glass in three dimensions with ± J near-neighbour interactions. The results are compared to other simulation data; we conclude that the damage spreading method can provide good estimates of the transition temperatures in this type of system. A discussion is given of phase transitions in spin glasses in terms of the geometry of phase space.
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.
By studying the time evolution of two configurations submitted to the same thermal noise, we investigate phase space properties of the three-dimensional ± J Ising spin glass. Our results for the distance between states are consistent with the picture of phase space having a multivalley structure below T c . By fixing the damage at one site, we also study the Hamming distance between the two configurations at its critical point, where the distribution of probability of getting damaged n times is found to be multifractal.
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.