For the large anisotropy system, h=1, the specific heat 
are shown for
several spin systems in Figure 6.15(a). The peak becomes sharper
and higher as the system size increases, indicating a divergent peak in an
infinite system, similar to the two-dimensional Ising model. Defining the
transition temperature 
at the peak of 
for the finite
system, the finite-size scaling theory [Landau:76a] predicts
that 
relates to 
through the scaling law
Setting 
, the Ising exponent, a good fit with 
, is
shown in Figure 6.15(b). A different scaling with the same
exponent for the correlation length,
is also satisfied quite well, resulting in 
. The
staggered magnetization drops down near 
, although the behaviors are
rounded off on these finite-size systems. All the evidence clearly
indicates that an Ising-like antiferromagnetic transition occurs at 
, with a divergent specific heat. In the smaller anisotropy case,
, similar behaviors are found. The scaling for the correlation length
is shown in Figure 6.16, indicating a transition at 
.
However, the specific heat remains finite at all temperatures.
Figure 6.15: (a) The Specific Heat for Different Size Systems of h=1. (b)
Finite Size Scaling for 
.
Figure 6.16: The Inverse Correlation Lengths for 
System
(
), 
System (
), and h=0 System
(
) for the Purpose of Comparison. The straight lines are the
scaling relation: 
. From it we can pin down
.
The most interesting case is 
(or 
, very close to those
in 
[Birgeneau:71a]). Figure 6.17 shows the
staggered correlation function at 
compared with those on the
isotropic model [Ding:90g]. The inverse correlation length measured,
together with those for the isotropic model (h=0), are shown in
Figure 6.16. Below 
, the Ising behavior of
a straight line becomes clear. Clearly, the system becomes
antiferromagnetically ordered around 
. The best estimate is
Figure 6.17: The Correlation Function on the 
System at 
for 
system. It decays with correlation length 
. Also shown is the isotropic case h=0, which has 
.