Related papers: The planted XY model: thermodynamics and inference
Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…
For many real spin-glass materials, the Edwards-Anderson model with continuous-symmetry spins is more realistic than the rather better understood Ising variant. In principle, the nature of an occurring spin-glass phase in such systems might…
We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP equations, originally derived by Parisi…
In this paper we study the Parisi variational problem for mixed $p$-spin glasses with Ising spins. Our starting point is a characterization of Parisi measures whose origin lies in the first order optimality conditions for the Parisi…
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…
We analyze the zero-temperature behavior of the XY Edwards-Anderson spin glass model on a square lattice. A newly developed algorithm combining exact ground-state computations for Ising variables embedded into the planar spins with a…
The ferromagnetic XY model on sparse random graphs in a randomly oriented field is analyzed via the belief propagation algorithm. At variance with the fully connected case and with the random field Ising model on the same topology, we find…
We study the problem of testing and recovering $k$-clique Ferromagnetic mean shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass model) with $n$ spins. The planted SK model -- a stylized mixture of an uncountable…
We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find…
The planted p-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic phase and a disordered phase with the latter splitting into many spin glass states at low temperatures. Conventional simulated…
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…
We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the single species case. The existence of the thermodynamic limit is…
We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain class of mixtures, the Parisi measure at zero temperature is…
We investigate an XY spin-glass model in which both spins and interactions (or couplings) evolve in time, but with widely separated time-scales. For large times this model can be solved using replica theory, requiring two levels of…
Numerical simulations of spin glass models with continuous variables set the problem of a reliable but efficient discretization of such variables. In particular, the main question is how fast physical observables computed in the discretized…
We analyze the infinite range Ising spin-glass in a transverse-field below the critical temperature by a one step replica symmetry theory(1S-RSB). The set of n replicas is divided in r blocks of m replicas each. We present results for…
In the present paper we have analysed a fermionic infinite-ranged quantum Heisenberg spin glass (s=1/2) with a BCS coupling in real space in the presence of an applied magnetic field. This model has been obtained by tracing out the…
We investigate dynamics of an inference algorithm termed the belief propagation (BP) when employed in spin glass (SG) models and show that its macroscopic behaviors can be traced by recursive updates of certain auxiliary field distributions…
The fermionic Ising spin glass models in a transverse field are investigated in a Grassmann path integral formalism. The Parisi's scheme of one-step replica symmetry breaking (RSB) is used within the static ansatz. This formalism has…
A generalization of the Sherrington-Kirkpatrick (SK) model for spin glasses is considered, in which the interaction matrix is endowed with a variance profile that has no particular structure an may be sparse. In the first part of this…