Related papers: Simultaneous replica-symmetry breaking for vector …
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…
Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a…
We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by…
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…
In this paper we review the predictions of the replica approach on the probability distribution of the overlaps among replicas and on the sample to sample fluctuations of this probability. We stress the role of replica equivalence in…
The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…
Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be…
We investigate the L\'evy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the…
So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking…
We study quantum spin systems with quenched Gaussian disorder. We prove that the variance of all physical quantities in a certain class vanishes in the infinite volume limit. We study also replica symmetry breaking phenomena, where the…
Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of $\pm J$ spin glasses at zero…
We apply the cavity method to a spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We show the correspondence with a replicated transfer matrix approach, up to the level…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…
Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the…
We study a 7-state Potts glass model in three dimensions with first, second, and third neighbor interactions with a bimodal distribution of couplings by Monte Carlo simulations. Our results show the existence of a spin-glass transition at a…
Physical quantities in the mixed $p$-spin glasses are evaluated with Nishimori's gauge theory and several variance inequalities. The $\mathbb Z_2$-symmetry breaking and the replica-symmetry breaking are studied in finite and infinite…
In a $p$-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change in the course of time. The spins are coupled to a heat bath with temperature $T$, while the coupling constants are coupled to a bath…
We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…
We show marginal stability of near-ground states in spherical spin glasses is equivalent to full replica symmetry breaking at zero temperature near overlap $1$. This connection has long been implicit in the physics literature, which also…
In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…