arXiv subjects

A. C. Carter

Publications and source records attributed to A. C. Carter.

3 recordsLinked to original sources

arXiv2003

On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents

Finite-size scaling (FSS) is a standard technique for measuring scaling exponents in spin glasses. Here we present a critique of this approach, emphasizing the need for all length scales to be large compared to microscopic scales. In particular we show that the replacement, in FSS analyses, of the correlation length by its asymptotic scaling form can lead to apparently good scaling collapses with the wrong values of the scaling exponents.

cond-mat.dis-nn↗

arXiv2002

The stiffness exponent of two-dimensional Ising spin glasses for non-periodic boundary conditions using aspect-ratio scaling

We study the scaling behavior of domain-wall energies in two-dimensional Ising spin glasses with Gaussian and bimodal distributions of the interactions and different types of boundary conditions. The domain walls are generated by changing the boundary conditions at T=0 in one direction. The ground states of the original and perturbed system are calculated numerically by applying an efficient matching algorithm. Systems of size LxM with different aspect-ratios 1/8 <= L/M <= 64 are considered. For Gaussian interactions, using the aspect-ratio scaling approach, we find a stiffness exponent theta=-0.287(4), which is independent of the boundary conditions in contrast to earlier results. Furthermore, we find a scaling behavior of the domain-wall energy as predicted by the aspect-ratio approach. Finally, we show that this approach does not work for the bimodal distribution of interactions.

cond-mat.dis-nn↗

arXiv2001

Aspect-Ratio Scaling and The Stiffness Exponent $θ$ for Ising Spin Glasses

We introduce the technique of aspect-ratio scaling to study the scale-dependence of interfacial energies in Ising spin glasses, and we show how one can use it to determine the stiffness exponent $θ$ in a clean way, with results that are independent of the domain-wall-forcing boundary conditions imposed on the system. In space dimension d=2 we obtain $θ= -0.282(3)$ for a Gaussian distribution of exchange interactions.

cond-mat.dis-nn↗