Hyperscaling violation in Ising Spin Glasses

Abstract

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.

5 pages, 9 figures

References in corpus (5)

• Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model
• An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses
• Finite size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation
• The bimodal and Gaussian Ising Spin Glasses in dimension two revisited
• Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant