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Register a new userNonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
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Added by
Victor Martin-Mayor
Publication date
2008
fields
Physics
and research's language is
English
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We study numerically the nonequilibrium dynamics of the Ising Spin Glass, for a time that spans eleven orders of magnitude, thus approaching the experimentally relevant scale (i.e. {em seconds}). We introduce novel analysis techniques that allow to compute the coherence length in a model-independent way. Besides, we present strong evidence for a replicon correlator and for overlap equivalence. The emerging picture is compatible with non-coarsening behavior.
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Spin Glasses (SG) are paradigmatic models for physical, computer science, biological and social systems. The problem of studying the dynamics for SG models is NP hard, i.e., no algorithm solves it in polynomial time. Here we implement the optical simulation of a SG, exploiting the N segments of a wavefront shaping device to play the role of the spin variables, combining the interference at downstream of a scattering material to implement the random couplings between the spins (the J ij matrix) and measuring the light intensity on a number P of targets to retrieve the energy of the system. By implementing a plain Metropolis algorithm, we are able to simulate the spin model dynamics, while the degree of complexity of the potential energy landscape and the region of phase diagram explored is user-defined acting on the ratio the P/N = alpha. We study experimentally, numerically and analytically this peculiar system displaying a paramagnetic, a ferromagnetic and a SG phase, and we demonstrate that the transition temperature T g to the glassy phase from the paramagnetic phase grows with alpha. With respect to standard in silico approach, in the optical SG interaction terms are realized simultaneously when the independent light rays interferes at the target screen, enabling inherently parallel measurements of the energy, rather than computations scaling with N as in purely in silico simulations.
We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1,+1}, are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.
The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, ...) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is never reached in macroscopic samples: in analogy with living beings, glasses are said to age. Here, we show how to relate experimentally relevant quantities with the experimentally unreachable low-temperature equilibrium phase. We have performed a very accurate computation of the non-equilibrium fluctuation-dissipation ratio for the three-dimensional Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. The resulting quantitative statics-dynamics dictionary, based on observables that can be measured with current experimental methods, could allow the experimental exploration of important features of the spin-glass phase without uncontrollable extrapolations to infinite times or system sizes.
Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear to take up a universal form for all spin glasses. The implications for the fundamental physics of transitions in complex systems are addressed.
The standard two-dimensional Ising spin glass does not exhibit an ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as $(1+r^2)^{-a/2}$, $a>0$. We study numerically with exact algorithms the ground state and domain wall excitations. Our results indicate that the inclusion of bond correlations does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro/antiferromagnetic domains into the system. The length scale of ferro/antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, $a to a_c = 0$. Thus, our results suggest that the system becomes a ferro/antiferromagnet only in the limit $a to 0$.
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