Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

Castellani, Tommaso; Krząkała, Florent; Ricci-Tersenghi, Federico

doi:10.1140/epjb/e2005-00293-1

Cited by 35 publications

(72 citation statements)

References 24 publications

(47 reference statements)

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“…The result is shown in figure B1 where the spin-glass susceptibility diverges below this line. At zero temperature, the critical probability is calculated as p c = 11/12 in [27,32], which is reproduced by our numerical calculation at zero temperature as p c = 0.916 65 (5).…”

Section: Appendix B the Critical Condition Based On The Spin-glass Ssupporting

confidence: 72%

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Distribution of partition function zeros of the ±Jmodel on the Bethe lattice

Matsuda

Müller

Nishimori

et al. 2010

J. Phys. A: Math. Theor.

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The distribution of partition function zeros is studied for the ±J model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin-glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify how the spin-glass transition is characterized by the zeros of the partition function. It is also shown that in the spin-glass phase a continuous distribution of singularities touches the axes of real field and temperature.

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Section: Appendix B the Critical Condition Based On The Spin-glass Ssupporting

confidence: 72%

“…Indeed, it is suggested that the spin-glass phase in the RRG has the full RSB [27,28]. However, we should be careful because we have not directly seen the instability of a replica-symmetric solution in the Bethe lattice of our definition.…”

Section: Behaviour Of the Two-dimensional Distribution Of Zerosmentioning

confidence: 85%

Distribution of partition function zeros of the ±Jmodel on the Bethe lattice

Matsuda

Müller

Nishimori

et al. 2010

J. Phys. A: Math. Theor.

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show abstract

“…So on the right of the cusp we have an unmagnetised spin glass phase, while on the left we have a mixed phase, i. e. spin glass with nonzero magnetization, usual for disordered systems with a directional bias in the couplings or in the external field. It is worth reminding that the location of this phase transition is only approximate, as one should use an ansatz with RSB in order to compute it exactly [46].…”

Section: Extrapolation In Qmentioning

confidence: 99%

The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism

Lupo

Parisi

Ricci-Tersenghi

2019

J. Phys. A: Math. Theor.

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The ferromagnetic XY model on sparse random graphs in a randomly oriented field is analyzed via the belief propagation algorithm. At variance with the fully connected case and with the random field Ising model on the same topology, we find strong evidences of a tiny region with Replica Symmetry Breaking (RSB) in the limit of very low temperatures. This RSB phase is robust against different choices of the external field direction, while it rapidly vanishes when increasing the graph mean degree, the temperature or the directional bias in the external field. The crucial ingredients to have such a RSB phase seem to be the continuous nature of vector spins, mostly preserved by the O(2)-invariant random field, and the strong spatial heterogeneity, due to graph sparsity. We also uncover that the ferromagnetic phase can be marginally stable despite the presence of the random field. Finally, we study the proper correlation functions approaching the critical points to identify the ones that become more critical.arXiv:1902.07132v2 [cond-mat.dis-nn]

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“…57 Its presence has been confirmed in the ±J Ising model on a Bethe lattice. 58 However, there is no evidence of a mixed phase in the ±J Ising model on a cubic lattice 55 and in related models. 59 In particular, the numerical results of Ref.…”

Section: Ising Spin Glass Systems a The ±J Edwards-anderson Isinmentioning

confidence: 99%

Critical behavior of three-dimensional Ising spin glass models

Pelissetto²,

2008

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We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin-glass models on cubic lattices of size L: the ±J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p = 0.5 and p = 0.7 (up to L = 28 and L = 20, respectively), and the bond-diluted bimodal model for bond-occupation probability p b = 0.45 (up to L = 16). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent ω related to the leading irrelevant operator: ω = 1.0(1). Shorter Monte Carlo simulations of the bond-diluted bimodal models at p b = 0.7 and p b = 0.35 (up to L = 10) and of the Ising spinglass model with Gaussian bond distribution (up to L = 8) also support the existence of a unique Ising spin-glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents ν and η: we obtain ν = 2.45(15) and η = −0.375(10).

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Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations

Cited by 35 publications

References 24 publications

Distribution of partition function zeros of the ±Jmodel on the Bethe lattice

Distribution of partition function zeros of the ±Jmodel on the Bethe lattice

The random field XY model on sparse random graphs shows replica symmetry breaking and marginally stable ferromagnetism

Critical behavior of three-dimensional Ising spin glass models

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