Related papers: Spin Glasses
We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding…
Within the wide class of disordered materials, spin glasses occupy a special place because of their conceptually simple definition of randomly interacting spins. Their modelling has triggered spectacular developments of out-of-equilibrium…
We consider the statistical properties over disordered samples of the overlap distribution $P_{\cal J}(q)$ which plays the role of an order parameter in spin-glasses. We show that near zero temperature (i) the {\it typical} overlap…
We show that in mean-field spin glasses, a discontinuous breaking of replica symmetry at the critical inverse temperature $\beta_c$ implies the existence of an intermediate shattered phase. This confirms a prediction from physics regarding…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten-…
The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range…
We show that there is no need to modify the Parisi replica symmetry breaking ansatz, by working with $R$ steps of breaking and solving {\it exactly} the discrete stationarity equations generated by the standard ``truncated Hamiltonian" of…
The main result in this paper is motivated by the M\'ezard-Parisi ansatz which predicts a very special structure for the distribution of spins in diluted mean field spin glass models, such as the random K-sat model. Using the fact that one…
We introduce a mathematical framework based on simple combinatorial arguments (Kernel Representation) that allows to deal successfully with spin glass problems, among others. Let $\Omega^{N}$ be the space of configurations of an $N-$ spins…
The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking…
Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution…
We prove that, in mixed $p$-spin models of spin glasses, the location of the ground state is chaotic under small Gaussian perturbations. For the case of even $p$-spin models, this was shown by Chen, Handschy and Lerman [2018]. We rely on a…
We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. A close connection between open quantum dynamics and replica symmetry breaking is established, in…
We propose an indirect way of studying the fluctuation-dissipation relation in spin-glasses that only uses available susceptibility data. It is based on a dynamic extension of the Parisi-Toulouse approximation and a Curie-Weiss treatment of…
We develop a simple method to study the high temperature, or high external field, behavior of the Sherrington-Kirkpatrick mean field spin glass model. The basic idea is to couple two different replicas with a quadratic term, trying to push…
We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic…
The spontaneous supersymmetry-breaking that takes place in certain spin-glass models signals a particular fragility in the structure of metastable states of such systems. This fragility is due to the presence of at least one marginal mode…
We consider mean-field vector spin glasses with self-overlap correction. The limit of free energy is known to be the Parisi formula, which is an infimum over matrix-valued paths. We decompose such a path into a Lipschitz matrix-valued path…
We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed…