Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model

Details Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model

2006-03-27

arxiv.org/abs/cond-mat/0603729v2

Phys. Rev. B 75, 174415 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages with 15 figures, extensively revised

Scientific paper

10.1103/PhysRevB.75.174415

The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$ are studied. We are able to consider large samples of up to $320^2$ spins by using sophisticated matching algorithms. We study $L \times L$ systems, but we also consider $L \times M$ samples, for different aspect ratios $R = L / M$. We find that the scaling behavior of the ground-state energy and its sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le 1 - p_c$) are characterized by simple scaling functions. In particular, the fluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass region the average domain-wall energy converges to a finite nonzero value as the sample size becomes infinite, holding $R$ fixed. Here, large finite-size effects are visible, which can be explained for all $p$ by a single exponent $\omega\approx 2/3$, provided higher-order corrections to scaling are included. Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: the distribution of the domain-wall energies converges to a Gaussian for $R \to 0$, although the domain walls of neighboring subsystems of size $L \times L$ are not independent.

Affiliated with

Also associated with

No associations

Rating

Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D $\pm J$ Random-Bond Ising Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-462918