ID: cond-mat/9607132

Heisenberg Spin Glass on a Hypercubic Cell

July 18, 1996

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Energy landscape in three-dimensional Heisenberg spin glasses

March 29, 2015

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Marco Baity-Jesi
Disordered Systems and Neura...
Statistical Mechanics

Recent work suggests that Heisenberg spin glasses may belong to the same universality class than structural glasses. Indeed, finding a lattice equivalent for supercooled liquids would probably allow easier numerical and analytical studies, that may help to answer long-standing questions on the glass transition. Supercooled liquids have many peculiar behaviors that should be found in the paramagnetic phase of Heisenberg spin glasses if the analogy between the two systems holds...

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Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature

March 31, 2021

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Maria Chiara Angelini, Carlo Lucibello, Giorgio Parisi, Gianmarco Perrupato, ... , Rizzo Tommaso
Disordered Systems and Neura...
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The spin-glass transition in a field in finite dimension is analyzed directly at zero temperature using a perturbative loop expansion around the Bethe lattice solution. The loop expansion is generated by the $M$-layer construction whose first diagrams are evaluated numerically and analytically. The generalized Ginzburg criterion reveals that the upper critical dimension below which mean-field theory fails is $D_U \le 8$, at variance with the classical result $D_U = 6$ yielded...

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The Four-Dimensional XY Spin Glass

March 29, 1996

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S. University of Derby, UK Jain
Condensed Matter

The nearest-neighbour XY spin glass on a hypercubic lattice in four dimensions is studied by Monte Carlo simulations. A finite- size scaling analysis of the data leads to a finite temperature spin glass transition at $T_c=0.95\pm 0.15$. The critical exponents are estimated to be $\nu_{sg}=0.70\pm 0.10$ and \eta_{sg}=-0.28\pm 0.38$. The results imply that the lower critical dimensionality for the XY spin glass is less than four.

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Two models of spin glasses -- Ising versus Heisenberg

March 18, 2010

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Hikaru Kawamura
Disordered Systems and Neura...

Brief review is given on recent numerical research of the ordering of two typical models of spin glasses (SGs), the three-dimensional (3D) Ising SG and the 3D Heisenberg SG models. Particular attention is paid to the questions of whether there is a thermodynamic transition in zero field, what are the associated critical properties, what is the nature of the ordered state, particularly of a possible replica-symmetry breaking, and whether there is a thermodynamic transition in ...

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Quantum Spin Glasses in Finite Dimensions

July 13, 1995

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Heiko Rieger, A. Peter Young
Condensed Matter
High Energy Physics - Theory

The Ising spin glass model in a transverse field has a zero temperature phase transition driven solely by quantum fluctuations. This quantum phase transition occuring at a critical transverse field strength has attracted much attention recently. We report the progress that has been made via Monte Carlo simulations of the finite dimensional, short range model.

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Dynamical solutions of a quantum Heisenberg spin glass model

July 13, 2004

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M. Bechmann, R. Oppermann
Statistical Mechanics
Disordered Systems and Neura...

We consider quantum-dynamical phenomena in the $\mathrm{SU}(2)$, $S=1/2$ infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical self-consistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complementary approximation schemes are applied: one restricts the quantum spin dynamics t...

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Numerical Simulations of Finite Dimensional Spin Glasses Show a Mean Field like Behavior

September 15, 1997

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E. Cagliari, Italy Marinari
Disordered Systems and Neura...
Statistical Mechanics

I discuss results from numerical simulations of finite dimensional spin glass models, and show that they show all signatures of a mean field like behavior, basically coinciding with the one of the Parisi solution. I discuss the Binder cumulant, the probability distribution of the order parameter, the non self-averaging behavior. The determination of correlation function and of spatially blocked observables quantities helps in qualifying the behavior of the system.

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Spin Glasses on the Hypercube

November 24, 2009

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L. A. Fernandez, V. Martin-Mayor, ... , Seoane B.
Disordered Systems and Neura...
Statistical Mechanics

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the non trivial problem of generating these lattices. Afterwards, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our t...

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Quantum Spin Systems after DLS1978

March 6, 2006

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Bruno Nachtergaele
Mathematical Physics

In their 1978 paper, Dyson, Lieb, and Simon (DLS) proved the existence of Ne'el order at positive temperature for the spin-S Heisenberg antiferromagnet on the d-dimensional hypercubic lattice when either S >= 1 and d >= 3 or S=1/2 and d is sufficiently large. This was the first proof of spontaneous breaking of a continuous symmetry in a quantum model at finite temperature. Since then the ideas of DLS have been extended and adapted to a variety of other problems. In this paper...

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Mean-Field Theory of a Quantum Heisenberg Spin Glass

September 16, 1999

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Antoine Georges, Olivier Parcollet, Subir Sachdev
Disordered Systems and Neura...
Statistical Mechanics
Strongly Correlated Electron...

A full mean field solution of a quantum Heisenberg spin glass model is presented in a large-N limit. A spin glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S=0, and the various regimes in the spin glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum prob...

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