Search results for "Spin glass"

Retrieving infinite numbers of patterns in a spin-glass model of immune networks

2013

The similarity between neural and immune networks has been known for decades, but so far we did not understand the mechanism that allows the immune system, unlike associative neural networks, to recall and execute a large number of memorized defense strategies {\em in parallel}. The explanation turns out to lie in the network topology. Neurons interact typically with a large number of other neurons, whereas interactions among lymphocytes in immune networks are very specific, and described by graphs with finite connectivity. In this paper we use replica techniques to solve a statistical mechanical immune network model with `coordinator branches' (T-cells) and `effector branches' (B-cells), a…

Mixed Valence Materials: Prussian Blue Analogues of Reduced Dimensionality (Small 16/2012)

2012

Transversal spin freezing and re-entrant spin glass phases in chemically disordered Fe-containing perovskite multiferroics

2015

We propose experimental verification and theoretical explanation of magnetic anomalies in the complex Fe-contained double perovskite multiferroics like PbFe$_{1/2}$Nb$_{1/2}$O$_3$. The theoretical part is based on our model of coexistence of long-range magnetic order and spin glass in the above substances. In our model, the exchange interaction is anisotropic, coupling antiferromagnetically $z$ spin components of Fe$^{3+}$ ions. At the same time, the $xy$ components are coupled by much weaker exchange interaction of ferromagnetic sign. In the system with spatial disorder (half of corresponding lattice cites are occupied by spinless Nb$^{5+}$ ions) such frustrating interaction results in the…

Theory of glass transition in spin glasses, orientational glasses and structural glasses

2008

Theoretical concepts about the glass transition are briefly reviewed, and the test of these ideas by Monte Carlo simulations of simple lattice models is described, with an emphasis on isotropic and anisotropic orientational glasses, and the bond fluctuation model of polymer melts. It is suggested that orientational glasses do have an equilibrium phase transition at zero temperature (in d = 3 dimensions!) only, in contrast to the Ising spin glass which orders at nonzero temperature. A diverging glass correlation length is identified that is responsible for the anomalous slowing down. For the Potts glass, the divergence seems to be exponential, implying that the model is at its lower critical…

Simulation of Models for Isotropic and Anisotropic Orientational Glasses

1992

“Orientational glass” behavior is found when molecular crystals are randomly diluted, and quadrupole moments get frozen by random alignment of the molecules, similar to “spin glass” behavior of randomly diluted magnets. Monte Carlo simulation of lattice models where quadrupole moments interact with nearest neighbor Gaussian coupling is a unique tool to study this behavior. The time-dependent glass order parameter exhibits anomalously slow relaxation, compatible with the Kohlrausch-Williams-Watts (KWW) stretched exponential function. Both isotropic and anisotropic models exhibit in d=2 and d=3 spatial dimensions glass transitions at zero temperature only. While the glass correlation length a…

Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts

2002

The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents $\theta_{s} \approx -0.36$ in 2D and $\theta_{s} \approx +0.31$ in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than thr…

Critical behavior of short range Potts glasses

1993

We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T−2), and an algebraic singularity atT…

Chemical disorder and Pb207 hyperfine fields in the magnetoelectric multiferroic Pb(Fe1/2Sb1/2)O3 and its solid solution with Pb(Fe1/2Nb1/2)O3

2018

We report on the results of magnetic susceptibility, electron paramagnetic resonance, and $^{207}\mathrm{Pb}$ nuclear magnetic resonance (NMR) studies of the magnetoelectric multiferroic $\mathrm{Pb}(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{S}{\mathrm{b}}_{1/2}){\mathrm{O}}_{3}$ (PFS) ceramic, as well as its solid solution with $\mathrm{Pb}(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}){\mathrm{O}}_{3}$ (PFN) of different degrees of the 1:1 ordering of magnetic $\mathrm{F}{\mathrm{e}}^{3+}$ and nonmagnetic $\mathrm{S}{\mathrm{b}}^{5+}$ ions. The ordering has been studied by x-ray diffraction (XRD) and NMR methods. In particular, two spectral lines, originating from the ordered and dis…

Theories of the Structural Glass Transition

2005

Spin Glasses on Thin Graphs

1995

In a recent paper we found strong evidence from simulations that the Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed amean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the f…