Related papers: A diluted version of the perceptron model
In an important recent paper, \cite{FL}, S. Franz and M. Leone prove rigorous lower bounds for the free energy of the diluted $p$-spin model and the $K$-sat model at any temperature. We show that the results for these two models are…
We study the problem of learning the input-output map of a controlled vibrating plate with a composite structure from experimental measurements. Analytical modeling of this control system faces challenges due to the essential orthotropy and…
We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are…
The polarizability measures how the system responds to an applied electrical field. Computationally, there are many different ways to evaluate this tensorial quantity, some of which rely on the explicit use of the external perturbation and…
We develop a microscopic theory of finite-temperature spin-nematic orderings in three-dimensional spatially anisotropic magnets consisting of weakly-coupled frustrated spin-1/2 chains with nearest-neighbor and next-nearest-neighbor…
We study the magnetic excitation spectrum in three-dimensional diluted ferromagnetic nearest-neighbor systems down to the percolation threshold. The disorder effects resulting from the dilution are handled accurately within self-consistent…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
We consider the Ising perceptron model with N spins and M = N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a one-sided threshold function, it was shown by Talagrand (2000,…
Isotropic XY is considered. It describes interaction of quantum spins on 1-dimesional lattice. Alternatevly one can call the model XXO Hiesenberg antiferromagnet. We solved long standing problem of evaluation of temperature corelations. We…
The use of nuclear spins as physical sensing systems is disadvantaged by their low signal responsivity, particularly when compared to sensing techniques based on electron spins. This primarily results from the small nuclear gyromagnetic…
We consider classical $O(N)$ vector models in dimension three and higher and investigate the nature of the low-temperature expansions for their multipoint spin correlations. We prove that such expansions define asymptotic series, and derive…
We provide exact analytical expressions for the magnetic susceptibility function in the high temperature expansion for finite Heisenberg spin systems with an arbitrary coupling matrix, arbitrary single-spin quantum number, and arbitrary…
In this paper we present a study of magnetic order of quantum Heisenberg spins on pyrochlore type lattices: a lattice of corner sharing tetrahedra. We use the Cluster Variation Approximation with the tetrahedron as basic cluster. We find…
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…
Magnetic diffuse scattering -- the broad magnetic scattering features observed in neutron-diffraction data above a material's magnetic ordering temperature -- provides a rich source of information about the material's magnetic Hamiltonian.…
We present an analytic approach to study concurrent influence of quenched non-magnetic site-dilution and finiteness of the lattice on the 2D XY model. Two significant deeply connected features of this spin model are: a special type of…
The physics of interacting nuclear spins arranged in a crystalline lattice is typically described using a thermodynamic framework: a variety of experimental studies in bulk solid-state systems have proven the concept of a spin temperature…
We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the…
In a reaction to excite the resonant state followed by the sequential cluster-decay, the in-plane angular correlation method is usually applied to determine the spin of the mother nucleus. However, the correlation pattern exhibited in a…
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution…