Related papers: Zeros of the partition function and dynamical sing…
We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the…
We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an…
Lee-Yang (LY) zeros, points on the complex plane of physical parameters where the partition function goes to zero, have found diverse applications across multiple disciplines like statistical physics, protein folding, percolation, complex…
It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we…
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…
In a classical work of the 1950's, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic Ising model always lie on the unit circle in the complex magnetic field. Zeros of the…
Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent…
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 spectral form factor of quantum chaotic systems has the familiar `ramp $+$ plateau' form. Techniques to determine its form in the semiclassical or the thermodynamic limit have been devised, in both cases based on the average over an…
We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the steady-state response and…
At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic…
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…
We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show…
This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition…
A spin glass is a diluted magnetic material in which the magnetic moments are randomly interacting, with a huge number of metastable states which prevent reaching equilibrium. Spin-glass models are conceptually simple, but require very…
Equilibrium systems which exhibit a phase transition can be studied by investigating the complex zeros of the partition function. This method, pioneered by Yang and Lee, has been widely used in equilibrium statistical physics. We show that…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
We investigate numerically disorder chaos in spin glasses, i.e. the sensitivity of the ground state to small changes of the random couplings. Our study focuses on the Edwards-Anderson model in d=1,2,3 and in mean-field. We find that in all…
We establish a relationship between the zeros of the partition function in the complex mass plane and the spectral properties of the Dirac operator in QCD. This relation is derived within the context of chiral Random Matrix Theory and…
Phase transitions in spin glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the "community detection" problem when cast in terms of a…