Article
Mathematics, Applied
Eliran Subag
Summary: The paper focuses on spherical spin glasses with support[0,q], constructing paths to find ground-state energy points on the sphere using a greedy strategy. It provides an algorithm to solve this problem efficiently. Additionally, for full-RSB models with support[0,q], the correct lower bound on the free energy is proven by the authors.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
C. Itoi, Y. Sakamoto
Summary: Physical quantities in the mixed p-spin glasses are evaluated using Nishimori's gauge theory and several variance inequalities. Z2-symmetry breaking and replica-symmetry breaking (RSB) are studied in both finite and infinite dimensions. Bounds on the expectation of the square of the magnetization and spontaneous magnetization clarify properties of the paramagnetic and spin glass phases. The study proves that variances of ferromagnetic and spin glass order parameters vanish on the Nishimori line in the infinite volume limit, suggesting self-averaging of these order parameters. This self-averaging of the spin glass order parameter justifies the absence of RSB on the Nishimori line.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Multidisciplinary
Maria Chiara Angelini, Carlo Lucibello, Giorgio Parisi, Gianmarco Perrupato, Federico Ricci-Tersenghi, Tommaso Rizzo
Summary: This study analyzes the spin-glass transition in finite dimension at zero temperature, revealing crucial differences with classical results such as the upper critical dimension D-U >= 8 for mean-field theory failure.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mechanics
Giampaolo Folena, Pierfrancesco Urbani
Summary: We investigate the properties of a recently introduced spin glass model of soft spins, which is subjected to an anharmonic quartic local potential. Using mean field theory, we solve the model and show that, at low temperatures, it exhibits full replica symmetry breaking and is marginally stable at zero temperature. We further demonstrate that the marginally stable state arises from a combination of soft linear excitations and pseudogapped non-linear excitations, making the model a natural candidate for describing the phenomena observed in soft glasses.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Physics, Fluids & Plasmas
C. M. Newman, D. L. Stein
Summary: We propose an approach to understand the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. We review the concepts of flexibility, critical droplet, and related quantities, and discuss three models that provide an understanding of these quantities. We also connect our approach with the concept of disorder chaos and examine four proposed scenarios for the low-temperature spin glass phase.
Article
Physics, Multidisciplinary
Chigak Itoi, Yoshinori Sakamoto
Summary: This study employs Nishimori's gauge theory to investigate spontaneous symmetry breaking phenomena in the transverse field mixed p-spin glass model in finite dimensions. Useful identities in the gauge theory allow for the study of Z2-symmetry breaking. It is proven that ferromagnetic long-range order and spontaneous magnetization at an arbitrary temperature are bounded by those on the Nishimori line in the corresponding classical model. These bounds imply the absence of both ferromagnetic long-range order and spontaneous magnetization in the spin glass phase. It is also proven that the ferromagnetic susceptibility has an upper bound in the paramagnetic and spin glass phases.
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
(2023)
Article
Statistics & Probability
Eliran Subag
Summary: Excluding some special cases, computing the critical inverse-temperature beta c of a mixed p-spin spin glass model is a difficult task. The only known method to calculate its value for a general model requires the full power of the Parisi formula. On the other hand, an easy application of the second moment method to the partition function yields an explicit lower bound beta m <= beta c to the critical inverse-temperature. Interestingly, in the important case of the Sherrington-Kirkpatrick model beta m = beta c. In this work we consider the multi-species spherical mixed p-spin models without external field, and characterize by a simple condition the models for which the second moment method works in the whole replica symmetric phase, namely, models such that beta m = beta c. In particular, for those models we obtain the value of beta c.
ELECTRONIC JOURNAL OF PROBABILITY
(2023)
Article
Physics, Mathematical
Linda Albanese, Francesco Alemanno, Andrea Alessandrelli, Adriano Barra
Summary: Understanding the glassy nature of neural networks is crucial for advancements in Machine Learning and Theoretical Artificial Intelligence. This paper focuses on dense associative Hebbian neural networks and develops mathematical approaches to address the phenomenon of replica symmetry breaking, allowing for a deeper insight into the glassiness they exhibit. The findings reveal a significant diversity in the underlying glassiness of these networks, particularly in comparison to traditional pairwise Hopfield models.
JOURNAL OF STATISTICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
C. M. Newman, N. Read, D. L. Stein
Summary: We study short-range Ising spin glasses in equilibrium at infinite system size, and demonstrate that, for a fixed bond realization and a Gibbs state drawn from a suitable metastate, all translation and locally invariant functions of a single pure state in the decomposition of the Gibbs state have the same value for all the pure states in that Gibbs state. We discuss various significant applications to spin glasses.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Multidisciplinary
Chigak Itoi
Summary: It has been rigorously proven that in the Edwards-Anderson spin glass model, the ground state is unique in any dimension for almost all continuous random exchange interactions when a single spin breaks the global Z(2) symmetry. This theorem implies that replica symmetry breaking does not occur at zero temperature, with site- and bond-overlaps concentrated at their maximal values. Short range spin glass models exhibit behaviors near zero temperature that are significantly different from mean field spin glass models.
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
(2021)
Article
Physics, Mathematical
Antonio Auffinger, Qiang Zeng
Summary: We investigate the topology of level sets of a smooth random field on R-N, which represents the energy landscape of a single particle on a random potential. Our study derives asymptotic formulas for the mean number of critical points with critical values in a given open set as the dimension N tends to infinity. A companion paper complements this analysis by providing the same study for the number of critical points with a given index.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
I. Paga, Q. Zhai, M. Baity-Jesi, E. Calore, A. Cruz, C. Cummings, L. A. Fernandez, J. M. Gil-Narvion, I. Gonzalez-Adalid Pemartin, A. Gordillo-Guerrero, D. Iniguez, G. G. Kenning, A. Maiorano, E. Marinari, V. Martin-Mayor, J. Moreno-Gordo, A. Munoz-Sudupe, D. Navarro, R. L. Orbach, G. Parisi, S. Perez-Gaviro, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, S. F. Schifano, D. L. Schlagel, B. Seoane, A. Tarancon, D. Yllanes
Summary: This paper investigates the microscopic origin of nonlinear dynamics in spin glasses by examining the time development of the spin-glass correlation length. The authors find a violation of the extended principle of superposition and observe differences in the correlation lengths between zero-field-cooled and thermoremanent magnetization as the magnetic field increases.
Article
Optics
Edwin D. Coronel, Avishek Das, Manoel L. da Silva-Neto, Ivan R. R. Gonzalez, Anderson S. L. Gomes, Ernesto P. Raposo
Summary: In this study, the statistical properties of intensity fluctuations in a multimode Q-switched Nd:yttrium aluminum garnet laser were investigated using a modified Pearson correlation coefficient. It was found that above threshold, the system exhibits a photonic ferromagnetic-like spontaneous mode-locking phase with replica symmetry breaking. Different from photonic glassy phase in random lasers, a relevant fraction of modes oscillate coherently in this system, but the synchronous oscillation of some modes is frustrated with the replica symmetry breaking.
Article
Physics, Multidisciplinary
Jonathan B. Curtis, Nicholas R. Poniatowski, Yonglong Xie, Amir Yacoby, Eugene Demler, Prineha Narang
Summary: A recent experiment demonstrated that proximity-induced Ising spin-orbit coupling can enhance spin-triplet superconductivity in Bernal bilayer graphene. However, the fluctuations of the spin orientation of the triplet order parameter in graphene suppress the superconducting transition to nearly zero temperature due to its perfect spin rotation symmetry. Both Ising spin-orbit coupling and an in-plane magnetic field can eliminate these fluctuations, significantly increasing the transition temperature, as supported by our analysis and consistent with the experiment. Our model also suggests the existence of a phase with quasilong-range ordered spin-singlet charge 4e superconductivity at low anisotropy and magnetic field, while the triplet 2e superconducting order only exhibits short-ranged correlations. Relevant experimental signatures are discussed.
PHYSICAL REVIEW LETTERS
(2023)
Article
Mathematics, Applied
Eva Dierkes, Christian Offen, Sina Ober-Bloebaum, Kathrin Flasskamp
Summary: Recently, Hamiltonian neural networks (HNNs) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems, while preserving the symplectic system structure. However, preserving symmetries requires additional attention. In this research, HNN is enhanced with a Lie algebra framework to detect and embed symmetries in the neural network, allowing simultaneous learning of the symmetry group action and the total energy of the system. Illustrative examples include a pendulum on a cart and a two-body problem from astrodynamics.