Related papers: Low Temperature Mass Spectrum in the Ising Spin Gl…
We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at…
We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$. For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of…
The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the…
Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a…
The long-range one-dimensional Ising spin-glass with random couplings decaying as $J(r) \propto r^{-\sigma}$ presents a spin-glass phase $T_c(\sigma)>0$ for $0 \leq \sigma<1$ (the limit $\sigma=0$ corresponds to the mean-field SK-model). We…
Numerical results for the local field distributions of a family of Ising spin-glass models are presented. In particular, the Edwards-Anderson model in dimensions two, three, and four is considered, as well as spin glasses with long-range…
According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to…
We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available results for classical vector spin glasses by an…
We study the low-temperature phase of the three-dimensional $\pm J$ Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T=0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated…
The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to the model with a general random exchange interactions. The relation between the expectation value of the…
We report large effects of Parisi replica permutation symmetry breaking (RPSB) on elementary excitations of fermionic systems with frustrated magnetic interactions. The electronic density of states is obtained exactly in the zero…
The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by…
We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip…
We investigate the replica symmetry broken (RSB) phase of spin glass (SG) models in a random field defined on Bethe lattices at zero temperature. From the properties of the RSB solution we deduce a closed equation for the extreme values of…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
We present numerical results for finite-temperature $T>0$ thermodynamic quantities, entropy $s(T)$, uniform susceptibility $\chi_0(T)$ and the Wilson ratio $R(T)$, for several isotropic $S=1/2$ extended Heisenberg models which are prototype…
At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx…
We study the replica symmetry breaking (RSB) in the Gaussian Unitary Ensemble (GUE) random matrix model. We find that the RSB occurs at the transition temperature $T_{\text{RSB}}\sim N^{-2/3}$ in the large $N$ limit. We argue that this…