In the literature the most frequently cited data are quite contradictory, and there is no consensus on the global minimum value of 2D Edwards-Anderson (2D EA) Ising model. By means of computer simulations, with the help of exact polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum depth in 2D EA-type models. We found a dependence of the global minimum depth on the dimension of the problem N and obtained its asymptotic value in the limit $N\to\infty$. We believe these evaluations can be further used for examining the behavior of 2D Bayesian models often used in machine learning and image processing.
We calculate the joint min--max distribution and the Edwards-Anderson's order parameter for the circular model of $1 / f$-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for min…
We numerically study the three-dimensional Edwards-Anderson model with Gaussian couplings, focusing on the heterogeneities arising in its nonequilibrium dynamics. Results are analyzed in terms of the backbone picture, which links strong dynamical heterogeneities to spatial heterogeneities emerging from the correlation of local rigidity of the bond network. Different two-times quantities as the flipping time distribution and the correlation and response functions, are evaluated over the full system and over high- and low-rigidity regions. We find that the nonequilibrium dynamics of the model is…
Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model"
最近的一篇有趣的论文[Yucesoy等人，Phys. Rev. Lett. 109，177204（2012），arXiv：1206：0783]将3D Edwards-Anderson（EA）模型的低温相与其平均场对应物Sherrington-Kirkpatrick（SK）模型进行了比较。研究了重叠分布P_J（q），得出了两种模型表现不同的结论.在这里，我们注意到，使用最先进的EA模型（用Janus计算机生成）的更大数据集进行的类似分析导致对Yucesoy等人的结果的非常清晰的解释，表明EA模型的行为与复本对称性破缺（RSB）理论所预测的一样。
Comment on "Ultrametricity in the Edwards-Anderson Model"
在最近的一封有趣的信中，康图奇{ \it et al.}已经研究了三维（3d）Edwards-Anderson（EA）Ising自旋玻璃的若干性质。他们声称已经找到了强有力的数值证据，证明存在一个复杂的超度量结构，类似于平均场模型的复本对称性破缺解所描述的结构。通过数值模拟，我们证明了Contucci { \it et al.}作为三维EA模型中的超度量结构的证据，在二维EA模型中得到了类似的精度，二维EA模型由液滴图像很好地描述，并且在有限温度下没有自旋玻璃相。我们得出结论，在Contucci { \it et al.}信不足以排除这种可能性，例如，液滴模型可以描述3dEA模型的行为。
The three-dimensional Edwards-Anderson spin-glass model present strong spatial heterogeneities well characterized by the so-called backbone, a magnetic structure that arises as a consequence of the properties of the ground state and the low-excitation levels of such a frustrated Ising system. Using extensive Monte Carlo simulations and finite size scaling, we study how these heterogeneities affect the phase transition of the model. Although, we do not detect any significant difference between the critical behavior displayed by the whole system and that observed inside and outside the backbone,…
An analytical application of Niedermayer's algorithm to the Edwards-Anderson model: analytical results for the multicritical point on the Nishimori line
Reply to Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model"
In Phys. Rev. Lett. 110，219701（2013）[arXiv：1211.0843] Billoire等人批评我们的信的结论[Phys. Rev. Lett. 109，177204（2012），arxiv：1206.0783]。他们认为在相同的温度下考虑爱德华-安德森和谢林顿-柯克帕特里克模型是不合适的，并提出了一种基于复本对称性破缺理论的解释。在这里，我们表明，在评论中提出的理论不能解释我们的数据上的爱德华-安德森自旋玻璃，我们坚持我们的断言，爱德华-安德森自旋玻璃模型的低温行为似乎不是平均场。
It is proven rigorously that the ground state in the Edwards-Anderson spin glass model is unique in any dimension for almost all continuous random exchange interactions under a condition that a single spin breaks the global ${\mathbb Z}_2$ symmetry. This theorem implies that replica symmetry breaking does not occur at zero temperature. The site- and bond-overlap are concentrated at their maximal values. It is argued that behaviors of short range spin glass models are much different from those of mean field spin glass models near zero temperature. Errata have been attached at the final page.
We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of the Edwards Anderson model, though with large uncertainties. In three dimensions, evidence for a finite-temperature transition, as occurs in the Edwards-Anderson model, is rather weak. This may indicate that the sizes are too small to probe the asymptotic critical behavior, or possibly that the universality class is different from that of the Edwards-Anderson…
We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a Generalized Belief Propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter $y$, and that the Kikuchi approximation of this generalized free ener…
The question of the number of thermodynamic states present in the low-temperature phase of the three-dimensional Edwards-Anderson Ising spin glass is addressed by studying spin and link overlap distributions using population annealing Monte Carlo simulations. We consider overlaps between systems with the same boundary condition-which are the usual quantities measured-and also overlaps between systems with different boundary conditions, both for the full systems and also within a smaller window within the system. Our results appear to be fully compatible with a single pair of pure states such a…
The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the Edwards-Anderson Ising spin-glass model for up to six space dimensions. We find that for five or less space dimensions, the fractal dimension is less than the space dimension. This means that interfaces are not space filling, thus implying replica symmetry breaking is absent in space dimensions fewer than six. However, the fractal dimension approaches the space …
With the advent of spatially resolved fluorescence imaging in quantum gas microscopes, it is now possible to directly image glassy phases and probe the local effects of disorder in a highly controllable setup. Here we present numerical calculations using a spatially-resolved local mean-field theory, show that it captures the essential physics of the disordered system and use it to simulate the density distributions seen in single-shot fluorescence microscopy. From these simulated images we extract local properties of the phases which are measurable by a quantum gas microscope and show that una…
