Excitations of the bimodal Ising spin glass on the brickwork lattice

Poulter, J.

doi:10.1088/1367-2630/11/6/063039

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…The Ising model with bimodal disorder has been extensively studied in the past. 4,5,7,[20][21][22][23][24][25][26][27] It is reasonably well established that no glassy phase exists for T > 0. 22,23 It has, however, been established that a glassy phase appears at zero temperature in this model.…”

Section: A Ising Modelmentioning

confidence: 99%

Thermodynamics of two-dimensional spin models with bimodal random-bond disorder

Tang

Iyer

Rigol³

2015

Phys. Rev. B

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We use numerical linked cluster expansions to study thermodynamic properties of the twodimensional classical Ising, quantum XY, and quantum Heisenberg models with bimodal randombond disorder on the square and honeycomb lattices. In all cases, the nearest-neighbor coupling between the spins takes values ±J with equal probability. We obtain the disorder averaged (over all disorder configurations) energy, entropy, specific heat, and uniform magnetic susceptibility in each case. These results are compared with the corresponding ones in the clean models. Analytic expressions are obtained for low orders in the expansion of these thermodynamic quantities in inverse temperature.

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Section: A Ising Modelmentioning

confidence: 99%

Thermodynamics of two-dimensional spin models with bimodal random-bond disorder

Tang

Iyer

Rigol³

2015

Phys. Rev. B

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Replica Cluster Variational Method

et al. 2010

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We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi's Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a variational expression of the replicated free energy of a system with quenched disorder, both averaged and on a single sample, and make the hierarchical ansatz using functionals of functions of fields to represent the messages. We obtain a set of integral equations for the message functionals. The main difference with the Bethe case is that the functionals appear in the equations in implicit form and are not positive definite, thus standard iterative population dynamic algorithms cannot be used to determine them. In the simplest cases the solution could be obtained iteratively using Fourier transforms. We begin to study the method considering the plaquette approximation to the averaged free energy of the Edwards-Anderson model in the paramagnetic Replica-Symmetric phase. In two dimensions we find that the spurious spin-glass phase transition of the Bethe approximation disappears and the paramagnetic phase is stable down to zero temperature on the square lattice for different random interactions. The quantitative estimates of the free energy and of various other quantities improve those of the Bethe approximation. The plaquette approximation fails to predict a second-order spin-glass phase transition on the cubic 3D lattice but yields good results in dimension four and higher. We provide the physical interpretation of the beliefs in the replica-symmetric phase as disorder distributions of the local Hamiltonian. The messages instead do not admit such an interpretation and indeed they cannot be represented as populations in the spin-glass phase at variance with the Bethe approximation. The approach can be used in principle to study the phase diagram of a wide range of disordered systems and it is also possible that it can be used to get quantitative predictions on single samples. These further developments present however great technical challenges

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Ground States of Two-Dimensional Ising Spin Glasses: Fast Algorithms, Recent Developments and a Ferromagnet-Spin Glass Mixture

Hartmann

2011

J Stat Phys

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Excitations of the bimodal Ising spin glass on the brickwork lattice

Cited by 3 publications

References 27 publications

Thermodynamics of two-dimensional spin models with bimodal random-bond disorder

Thermodynamics of two-dimensional spin models with bimodal random-bond disorder

Replica Cluster Variational Method

Ground States of Two-Dimensional Ising Spin Glasses: Fast Algorithms, Recent Developments and a Ferromagnet-Spin Glass Mixture

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