Related papers: Replica Symmetry Breaking without Replicas
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…
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a transverse magnetic field if the temperature…
Considering the unphysical result obtained in the calculation of the free-energy cost for twisting the boundary conditions in a spin glass, we trace it to the negative multiplicities associated with the Parisi replica-symmetry breaking…
We give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of G=O(n+1,1) and G'=O(n,1). We construct three meromorphic families of the symmetry breaking…
An infinite range spin glass like model for granular systems is introduced and studied through the replica mean field formalism. Equilibrium, density dependent properties under vibration and gravity are obtained.
In this review we define and discuss metastates, mathematical tools with general applicability to thermodynamic systems which are particularly useful when working with disordered or inhomogeneous short-range systems. In an infinite such…
Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…
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…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
The spin and the chirality orderings of the three-dimensional Heisenberg spin glass with the weak random anisotropy are studied under applied magnetic fields by equilibrium Monte Carlo simulations. A replica symmetry breaking transition…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we…
The one-step replica symmetry breaking (RSB) is used to study a two-sublattice fermionic infinite-range Ising spin glass (SG) model in a transverse field $\Gamma$. The problem is formulated in a Grassmann path integral formalism within the…
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…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We propose an ultrametric broken replica symmetry trial function for the diluted mean field sping glass model in the framework of random multi-overlap structure.
Spin glass theory, as a paradigm for describing disordered magnetic systems, constitutes a prominent subject of study within statistical physics. Replica symmetry breaking (RSB), as one of the pivotal concepts for the understanding of spin…
In the study of disordered models like spin glasses the key object of interest is the rugged energy hypersurface defined in configuration space. The statistical mechanics calculation of the Gibbs-Boltzmann Partition Function gives the…