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Concept

Spin glass

Summary

In condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called 'freezing temperature' Tf. In ferromagnetic solids, component atoms' magnetic spins all align in the same direction. Spin glass when contrasted with a ferromagnet is defined as "disordered" magnetic state in which spins are aligned randomly or without a regular pattern and the couplings too are random. The term "glass" comes from an analogy between the magnetic disorder in a spin glass and the positional disorder of a conventional, chemical glass, e.g., a window glass. In window glass or any amorphous solid the atomic bond structure is highly irregular; in contrast, a crystal has a uniform pattern of atomic bonds. In ferromagnetic solids, magnetic spins all align in the same direction; this is analogous to a crystal's lattice-based structure. The individual atomic bonds in a spin glass are a mix

Official source

https://en.wikipedia.org/wiki/Spin_glass

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From quantum glass to addressable spin clusters in the model magnet LiHoxY1−xF4

Tatjana Hählen

This report describes an AC-susceptibility study on

LiHo_xY_{1−x}F_4

LiHo_xY_{1−x}F_4 has different phases depending on the concentration x of holmium. Pure

LiHoF_4

is a ferromagnet, at concentrations of

x \approx 0.20

it is a spin glass and at concentrations of

x \approx 0.05

it becomes a spin liquid. The crystal studied here is

LiHo_ {0.04}Y_{0.96}F_4. In this spin liquid phase it shows several interesting properties which differ from ordinary spin glasses. Its spectral width of the imaginary part of the magnetic susceptibility

\chi^{''} narrows with decreasing temperature contrary to spin glasses. We measured the real

\chi^{'}

and the imaginary part

\chi^ {''}

of the magnetic susceptibility at different temperature and over a frequency range of 5 decades. The data are an extension to higher temperature of already existing data and match well with them in the overlapping temperatures. Our data shows well the trend the shift of the peak of the response function for

\chi^{''}

to higher frequencies and the decrease of the peak amplitude with increasing temperature. Also the cut of frequency for

\chi^ {'}$ increases with temperature. This is in agreement with the existing data at lower temperature.

2007

Parallel retrieval of correlated patterns: From Hopfield networks to Boltzmann machines

Andrea De Antoni

In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a modification of the Hebbian prescription, which induces a coupling between consecutive patterns and this effect is tuned by a parameter a. In the latter case, dilution is introduced in pattern entries, in such a way that a fraction d of them is blank. Then, we merge these two extensions to obtain a system able to retrieve several patterns in parallel and the quality of retrieval, encoded by the set of Mattis magnetizations {m(mu)}, is reminiscent of the correlation among patterns. By tuning the parameters d and a, qualitatively different outputs emerge, ranging from highly hierarchical to symmetric. The investigations are accomplished by means of both numerical simulations and statistical mechanics analysis, properly adapting a novel technique originally developed for spin glasses, i.e. the Hamilton-Jacobi interpolation, with excellent agreement. Finally, we show the thermodynamical equivalence of this associative network with a (restricted) Boltzmann machine and study its stochastic dynamics to obtain even a dynamical picture, perfectly consistent with the static scenario earlier discussed. (c) 2012 Elsevier Ltd. All rights reserved.

Elsevier2013

We explore two methods for single-crystal growth of the theoretically proposed magnetic Weyl semimetals RAlGe (R = Pr, Ce), which prove that a floating-zone technique, being both crucible- and flux-free, is crucial to obtain perfectly stoichiometric RAlGe crystals. In contrast, the crystals grown by a flux-growth technique tend to be Al-rich. We further present both structural and elemental analyses, along with bulk magnetization and electrical resistivity data on the crystals prepared by the floating-zone technique. Both systems with the intended 1:1:1 stoichiometry crystallize in the anticipated polar I4(1) md (No. 109) space group, although neither displays the theoretically expected ferromagnetic ground state. Instead PrAlGe displays a spin-glass-like transition below 16 K with an easy c axis and CeAlGe has an easy-ab-plane antiferromagnetic order below 5 K. The grown crystals provide an ideal platform for microscopic studies of the magnetic field-tunable correlation physics involving magnetism and topological Weyl nodes.

AMER PHYSICAL SOC2019