Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D ±J Ising Spin Glass
Abstract
The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and -1 bonds are studied for
L×L
square lattices with
L≤48
, and
p
= 0.5, where
p
is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. When
L
is even, almost all domain walls have energy
E
dw
= 0 or 4. When
L
is odd, most domain walls have
E
dw
= 2. The probability distribution of the entropy,
S
dw
, is found to depend strongly on
E
dw
. When
E
dw
=0
, the probability distribution of
|
S
dw
|
is approximately exponential. The variance of this distribution is proportional to
L
, in agreement with the results of Saul and Kardar. For
E
dw
=k>0
the distribution of
S
dw
is not symmetric about zero. In these cases the variance still appears to be linear in
L
, but the average of
S
dw
grows faster than
L
−
−
√
. This suggests a one-parameter scaling form for the
L
-dependence of the distributions of
S
dw
for
k>0
.