We propose a new picture of the Ising-spin-glass phase, based on an Ansatz for the scaling of low-lying large-scale-droplet excitations. We find behavior very different from the infinite-range model. The truncated spatial correlations decay as a power of distance, the ac nonlinear susceptibility diverges as a power of $\mathrm{ln}\ensuremath{\omega}$, and the magnetization noise power diverges as $\frac{1}{\ensuremath{\omega}}$ with logarithmic corrections. A magnetic field destroys the spin-glass phase so that there is no de Almeida-Thouless transition. Defect excitations should yield similar dynamic phenomena in vector spin-glasses.We propose a new picture of the Ising-spin-glass phase, based on an Ansatz for the scaling of low-lying large-scale-droplet excitations. We find behavior very different from the infinite-range model. The truncated spatial correlations decay as a power of distance, the ac nonlinear susceptibility diverges as a power of $\mathrm{ln}\ensuremath{\omega}$, and the magnetization noise power diverges as $\frac{1}{\ensuremath{\omega}}$ with logarithmic corrections. A magnetic field destroys the spin-glass phase so that there is no de Almeida-Thouless transition. Defect excitations should yield similar dynamic phenomena in vector spin-glasses.

Physical Review LettersApr 14, 1986806 citations

Attempt at a Comprehensive Description of the Slow Spin Glass Dynamics

J. Hammann, Miguel Ocio, E. Vincent

NATO ASI series. Series B : PhysicsJan 1, 19905 citations

Finding spin glass ground states through deep reinforcement learning

Changjun Fan, Mutian Shen, Zohar Nussinov +3 more

Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for the understanding of the nature of disordered magnetic and other physical systems, but also useful to solve a broad array of hard combinatorial optimization problems across multiple disciplines. Despite decades-long efforts, an algorithm with both high accuracy and high efficiency is still lacking. Here we introduce DIRAC - a deep reinforcement learning framework, which can be trained purely on small-scale spin glass instances and then applied to arbitrarily large ones. DIRAC displays better scalability than other methods and can be leveraged to enhance any thermal annealing method. Extensive calculations on 2D, 3D and 4D Edwards-Anderson spin glass instances demonstrate the superior performance of DIRAC over existing methods. As many hard combinatorial optimization problems have Ising spin glass formulations, our results suggest a promising tool in solving these hard problems. Moreover, the presented algorithm will help us better understand the nature of the low-temperature spin-glass phase, which is a fundamental challenge in statistical physics.Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for the understanding of the nature of disordered magnetic and other physical systems, but also useful to solve a broad array of hard combinatorial optimization problems across multiple disciplines. Despite decades-long efforts, an algorithm with both high accuracy and high efficiency is still lacking. Here we introduce DIRAC - a deep reinforcement learning framework, which can be trained purely on small-scale spin glass instances and then applied to arbitrarily large ones. DIRAC displays better scalability than other methods and can be leveraged to enhance any thermal annealing method. Extensive calculations on 2D, 3D and 4D Edwards-Anderson spin glass instances demonstrate the superior performance of DIRAC over existing methods. As many hard combinatorial optimization problems have Ising spin glass formulations, our results suggest a promising tool in solving these hard problems. Moreover, the presented algorithm will help us better understand the nature of the low-temperature spin-glass phase, which is a fundamental challenge in statistical physics.

arXiv:2109.14411Sep 29, 20213 citations

Numerical and experimental studies of the dynamics of Ising spin glasses

Jan‐Olov Andersson

Jan 1, 19941 citation

Collapse of the waiting time effect in a spin glass

Daniel Tennant, R. Orbach

Waiting time measurements are reported for a bulk polycrystalline sample of the spin glass ${\mathrm{Cu}}_{0.95}{\mathrm{Mn}}_{0.05}$ . We observe a suppression of aging as the glass temperature is approached from below. These results are interpreted in terms of a spin-glass correlation length approaching and reaching crystallite sizes. They provide a direct experimental connection between the correlation length scale and relaxation times in the spin-glass state. In particular, these measurements track the value of the dynamic critical exponent as the system transitions from the critical temperature regime to its low-temperature, quasistatic nonequilibrium phase.Waiting time measurements are reported for a bulk polycrystalline sample of the spin glass ${\mathrm{Cu}}_{0.95}{\mathrm{Mn}}_{0.05}$. We observe a suppression of aging as the glass temperature is approached from below. These results are interpreted in terms of a spin-glass correlation length approaching and reaching crystallite sizes. They provide a direct experimental connection between the correlation length scale and relaxation times in the spin-glass state. In particular, these measurements track the value of the dynamic critical exponent as the system transitions from the critical temperature regime to its low-temperature, quasistatic nonequilibrium phase.

Physical review. B./Physical review. BMay 6, 20204 citations

Waiting time measurements are reported for a bulk polycrystalline sample of the spin glass

{\mathrm{Cu}}_{0.95}{\mathrm{Mn}}_{0.05}

. We observe a suppression of aging as the glass temperature is approached from below. These results are interpreted in terms of a spin-glass correlation length approaching and reaching crystallite sizes. They provide a direct experimental connection between the correlation length scale and relaxation times in the spin-glass state. In particular, these measurements track the value of the dynamic critical exponent as the system transitions from the critical temperature regime to its low-temperature, quasistatic nonequilibrium phase.