scholarly journals Lower critical dimension of Ising spin glasses

2001 ◽  
Vol 64 (18) ◽  
Author(s):  
A. K. Hartmann ◽  
A. P. Young
Keyword(s):  
Spin Glasses ◽  
Critical Dimension ◽  
Ising Spin

scholarly journals Non-perturbative effects in spin glasses

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Michele Castellana ◽  
Giorgio Parisi
Keyword(s):  
Fixed Point ◽  
Ising Model ◽  
Spin Glasses ◽  
Numerical Study ◽  
Mean Field ◽  
Critical Dimension ◽  
Upper Critical Dimension ◽  
Ising Spin ◽  
Ferromagnetic Ising Model ◽  
The Mean

Abstract We present a numerical study of an Ising spin glass with hierarchical interactions—the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to d ≥ 4 and d < 4 for the d-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the "Equation missing"-expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent ν in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only ~2% from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.

scholarly journals Hyperscaling Violation in Ising Spin Glasses

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 978
Author(s):  
Ian A. Campbell ◽  
Per H. Lundow
Keyword(s):  
Critical Exponents ◽  
Spin Glasses ◽  
Critical Dimension ◽  
Ising Models ◽  
Upper Critical Dimension ◽  
Random Interactions ◽  
Ising Spin ◽  
Ising Systems ◽  
Binder Cumulant ◽  
Hyperscaling Violation

In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D = 6 . Estimates are obtained for the “violation of hyperscaling exponent” values in the various models.

Damage Spreading in ±J Asymmetric Ising Spin Glasses

1995 ◽  
Vol 5 (3) ◽  
pp. 355-364 ◽  
Author(s):  
R. M.C. de Almeida ◽  
L. Bernadi ◽  
I. A. Campbell
Keyword(s):  
Spin Glasses ◽  
Damage Spreading ◽  
Ising Spin

scholarly journals Analysis of landscape hierarchy during coarsening and aging in Ising spin glasses

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Stefan Boettcher ◽  
Mahajabin Rahman
Keyword(s):  
Spin Glasses ◽  
Ising Spin

Monte Carlo renormalization-group study of Ising spin glasses

1988 ◽  
Vol 37 (13) ◽  
pp. 7745-7750 ◽  
Author(s):  
Jian-Sheng Wang ◽  
Robert H. Swendsen
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Spin Glasses ◽  
Ising Spin ◽  
Monte Carlo Renormalization Group

scholarly journals Ising Spin Glasses in a Magnetic Field

1999 ◽  
Vol 82 (24) ◽  
pp. 4934-4937 ◽  
Author(s):  
J. Houdayer ◽  
O. C. Martin
Keyword(s):  
Magnetic Field ◽  
Spin Glasses ◽  
Ising Spin
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