Condensed Matter

The recent renaissance in machine learning has brought about a plethora of new techniques in the study of condensed matter and statistical physics. In particular, artificial neural networks (ANNs) have been used extensively in the classification and identification of phase transitions in spin models; however, their applicability is typically limited to the spin models they are trained with and little is known about their generalizability. Here, we propose a method that resembles the introduction of sparsity, by which simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic q -state Potts model in different dimensions for q≥2 . We establish the generalizability of the ANNs by showing that critical properties are correctly reproduced, and show that the same method can also be applied to the highly nontrivial case of the antiferromagnetic q -state Potts model. Furthermore, we demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative spin configurations artificially constructed through symmetry considerations. Our findings suggest that nontrivial information of multiple-state systems can be encoded in a representation of far fewer states, and the amount of ANNs required in the study of spin models can potentially be reduced. We anticipate our methodology will invigorate the application and understanding of machine learning techniques to spin models and related fields.

A viscoelastic model is established to reveal the relation between alpha-beta relaxation of glass and the double-peak phenomenon in the experiments of impulse excited vibration. In the modelling, the normal mode analysis (NMA) of potential energy landscape (PEL) picture is employed to describe mechanical alpha and beta relaxations in a glassy material. The model indicates that a small beta relaxation can lead to an apparent double-peak phenomenon resulted from the free vibration of a glass beam when the frequency of beta relaxation peak is close to the natural frequency of specimen. The theoretical prediction is validated by the acoustic spectrum of a fluorosilicate glass beam excited by a mid-span impulse. Furthermore, the experimental results indicate a negative temperature-dependence of the frequency of beta relaxation in the fluorosilicate glass S-FSL5 which can be explained based on the physical picture of fragmented oxide-network patches in liquid-like regions.

We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse systems have more basins of attractions than the dynamics of densely connected ones, we consider the attractors of a greedy dynamics in sparse topologies, considered as proxy for the stored memories. We enumerate them using numerical simulation and extend the analysis to large systems sizes using belief propagation. We find that the logarithm of the number of such cycles is a non monotonic function of the mean connectivity and we discuss the similarities with biological neural networks describing the memory capacity of the hippocampus.

The structure of the first sharp diffraction peak (FSDP) of amorphous silicon ( a -Si) near 2 Angstrom −1 is addressed with particular emphasis on the position, intensity, and width of the diffraction curve. By studying a number of continuous random network (CRN) models of a -Si, it is shown that the position and the intensity of the FSDP are primarily determined by radial atomic correlations in the amorphous network on the length scale of 15 Angstroms. A shell-by-shell analysis of the contribution from different radial shells reveals that the key contributions to the FSDP originate from the second and fourth radial shells in the network, which are accompanied by a background contribution from the first shell and small residual corrections from the distant radial shells. The results from numerical calculations are complemented by a phenomenological discussion of the relationship between the peaks in the structure factor in the wavevector space and the reduced pair-correlation function in the real space. An approximate functional relation between the position of the FSDP and the average second-neighbor distance of Si atoms in the amorphous network is derived, which is corroborated by numerical calculations.

The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results which allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived through computing the Lyapunov exponents from Avila's global theory, and also numerically verified by calculating the fractal dimension. We further propose a novel scheme with experimental feasibility to realize our model based on an optical Raman lattice, which paves the way for experimental exploration of the predicted exact ME physics.

We obtain an exact analytic expression for the average distribution, in the thermodynamic limit, of overlaps between two copies of the same random energy model (REM) at different temperatures. We quantify the non-self averaging effects and provide an exact approach to the computation of the fluctuations in the distribution of overlaps in the thermodynamic limit. We show that the overlap probabilities satisfy recurrence relations that generalise Ghirlanda-Guerra identities to two temperatures. We also analyse the two temperature REM using the replica method. The replica expressions for the overlap probabilities satisfy the same recurrence relations as the exact form. We show how a generalisation of Parisi's replica symmetry breaking ansatz is consistent with our replica expressions. A crucial aspect to this generalisation is that we must allow for fluctuations in the replica block sizes even in the thermodynamic limit. This contrasts with the single temperature case where the extremal condition leads to a fixed block size in the thermodynamic limit. Finally, we analyse the fluctuations of the block sizes in our generalised Parisi ansatz and show that in general they may have a negative variance.

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.

Optimization plays a significant role in many areas of science and technology. Most of the industrial optimization problems have inordinately complex structures that render finding their global minima a daunting task. Therefore, designing heuristics that can efficiently solve such problems is of utmost importance. In this paper we benchmark and improve the thermal cycling algorithm [Phys. Rev. Lett. 79, 4297 (1997)] that is designed to overcome energy barriers in nonconvex optimization problems by temperature cycling of a pool of candidate solutions. We perform a comprehensive parameter tuning of the algorithm and demonstrate that it competes closely with other state-of-the-art algorithms such as parallel tempering with isoenergetic cluster moves, while overwhelmingly outperforming more simplistic heuristics such as simulated annealing.

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??a c =0 . Thus, our results suggest that the system becomes a ferro/antiferromagnet only in the limit a?? .

In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a one-particle problem in very high dimension to which we apply different theoretical methods tailored for high-dimensional lattices: the Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and the cavity method. Our results indicate the existence of two transition lines and three distinct dynamical phases: a completely many-body localized phase at low energy, a fully ergodic phase at high energy, and a multifractal "bad metal" phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space. We discuss the limitations of our approximations and the relationship with previous studies.