Rigorous lower bounds to critical exponents for ferromagnetic ising systems

1976 ◽  
Vol 33 (2) ◽  
pp. 591-596
Author(s):  
W. F. Wreszinski
Keyword(s):  
Lower Bounds ◽  
Critical Exponents ◽  
Ising Systems

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.

Critical exponents for Ising-like systems on Sierpinski carpets

1987 ◽  
Vol 48 (4) ◽  
pp. 553-558 ◽  
Author(s):  
B. Bonnier ◽  
Y. Leroyer ◽  
C. Meyers
Keyword(s):  
Critical Exponents ◽  
Sierpinski Carpets
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