The de Almeida–Thouless Line in Hierarchical Quantum Spin Glasses

AbstractWe determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model and its hierarchical generalization, the GREM. Our results extent known results both in the classical case of vanishing transversal field and in the quantum case for vanishing longitudinal field. Following Derrida and Gardner, we argue that the longitudinal field has to be implemented hierarchically also in the Quantum GREM. We show that this ensures the shrinking of the spin glass phase in the presence of the magnetic fields as is also expected for the Quantum Sherrington–Kirkpatrick model.

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Ergodic and localized regions in quantum spin glasses on the Bethe lattice

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2016.0424 ◽

2017 ◽

Vol 375 (2108) ◽

pp. 20160424 ◽

Cited By ~ 4

Author(s):

G. Mossi ◽

A. Scardicchio

Keyword(s):

Spin Glass ◽

Spin Glasses ◽

Quantum Dynamics ◽

Bethe Lattice ◽

Transverse Field ◽

Quantum Systems ◽

Quantum Spin ◽

Many Body ◽

Spin Glass Phase ◽

Ising Spin

By considering the quantum dynamics of a transverse-field Ising spin glass on the Bethe lattice, we find the existence of a many-body localized (MBL) region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split into a small MBL region and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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DISTRIBUTION OF PURE STATES IN SHORT-RANGE SPIN GLASSES

International Journal of Modern Physics B ◽

10.1142/s0217979210055779 ◽

2010 ◽

Vol 24 (14) ◽

pp. 2091-2106 ◽

Cited By ~ 3

Author(s):

C. M. NEWMAN ◽

D. L. STEIN

Keyword(s):

Spin Glasses ◽

Short Range ◽

Glass Phase ◽

Single Pair ◽

Mixed States ◽

Spin Glass Phase ◽

Kirkpatrick Model ◽

Pure States ◽

Mathematical Construct ◽

Infinite Range

We review the structure of the spin glass phase in the infinite-range Sherrington–Kirkpatrick model and the short-range Edwards–Anderson (EA) model. While the former is now believed to be understood, the nature of the latter remains unresolved. However, considerable insight can be gained through the use of the metastate, a mathematical construct that provides a probability measure on the space of all thermodynamic states. Using tools provided by the metastate construct, possibilities for the nature of the organization of pure states in short-range spin glasses can be considerably narrowed. We review the concept of the "ordinary" metastate, and also newer ideas on the excitation metastate, which has been recently used to prove existence of only a single pair of ground states in the EA Ising model in the half-plane. We close by presenting a new result, using metastate methods, on the number of mixed states allowed in the EA model.

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LONGITUDINAL FIELD µSR IN CuMn SPIN GLASSES BELOW Tf

Le Journal de Physique Colloques ◽

10.1051/jphyscol:19888472 ◽

1988 ◽

Vol 49 (C8) ◽

pp. C8-1035-C8-1036 ◽

Cited By ~ 1

Author(s):

H. Pinkvos ◽

F. N. Gygax ◽

E. Lippelt ◽

Ch. Schwink

Keyword(s):

Spin Glasses ◽

Longitudinal Field

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Quantum spin glasses with uniaxial exchange anisotropy

Physics Letters A ◽

10.1016/0375-9601(85)90069-6 ◽

1985 ◽

Vol 110 (7-8) ◽

pp. 415-419 ◽

Cited By ~ 2

Author(s):

B.W. Morris

Keyword(s):

Spin Glasses ◽

Quantum Spin ◽

Exchange Anisotropy

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XII.—On the Theory of Unimolecular Gas Reactions: A Quantum Harmonic Oscillator Model

Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences ◽

10.1017/s0080454100007421 ◽

1954 ◽

Vol 64 (2) ◽

pp. 161-174 ◽

Cited By ~ 1

Author(s):

N. B. Slater

Keyword(s):

High Pressure ◽

Classical Mechanics ◽

Classical Case ◽

Constant Factor ◽

Quantum Case ◽

Fundamental Vibration ◽

Fixed Temperature ◽

Dissociation Probability ◽

Pressure Scale ◽

Continuum Of States

SynopsisThe writer's theory of unimolecular dissociation rates, based on the treatment of the molecule as a harmonically vibrating system, is put in a form which covers quantum as well as classical mechanics. The classical rate formulæ are as before, and are also the high-temperature limits of the new quantum formulæ. The high-pressure first-order rate k∞ is found first from the Gaussian distribution of co-ordinates and momenta of harmonic systems, and is justified for the quantum-mechanical case by Bartlett and Moyal's phase-space distributions. This leads to a re-formulation of k∞ as a molecular dissociation probability averaged over a continuum of states, and to a general rate for any pressure of the gas.The high-pressure rate k∞ is of the form ve-F/kT, where v and F depend, in the quantum case, on the temperature T; but v is always between the highest and lowest fundamental vibration frequencies of the molecule. Concerning the decline of the general rate k with pressure at fixed temperature, k/k∞ is to a certain approximation the same function of as was tabulated earlier for the classical case, apart from a constant factor changing the pressure scale in the quantum case.

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