<s>
The	O
spherical	B-Algorithm
model	I-Algorithm
is	O
a	O
model	O
of	O
ferromagnetism	O
similar	O
to	O
the	O
Ising	O
model	O
,	O
which	O
was	O
solved	O
in	O
1952	O
by	O
T	O
.	O
H	O
.	O
Berlin	O
and	O
M	O
.	O
Kac	O
.	O
</s>
<s>
Berlin	O
and	O
Kac	O
saw	O
this	O
as	O
an	O
approximation	O
to	O
the	O
usual	O
Ising	O
model	O
,	O
arguing	O
that	O
the	O
-summation	O
in	O
the	O
Ising	O
model	O
can	O
be	O
viewed	O
as	O
a	O
sum	O
over	O
all	O
corners	O
of	O
an	O
N-dimensional	O
hypercube	B-Operating_System
in	O
-space	O
.	O
</s>
<s>
It	O
was	O
rigorously	O
proved	O
by	O
Kac	O
and	O
C	O
.	O
J	O
.	O
Thompson	O
that	O
the	O
spherical	B-Algorithm
model	I-Algorithm
is	O
a	O
limiting	O
case	O
of	O
the	O
N-vector	B-Algorithm
model	I-Algorithm
.	O
</s>
<s>
For	O
the	O
critical	O
temperature	O
occurs	O
at	O
absolute	B-Application
zero	I-Application
,	O
resulting	O
in	O
no	O
phase	O
transition	O
for	O
the	O
spherical	B-Algorithm
model	I-Algorithm
.	O
</s>
<s>
For	O
d	O
greater	O
than	O
2	O
,	O
the	O
spherical	B-Algorithm
model	I-Algorithm
exhibits	O
the	O
typical	O
ferromagnetic	O
behaviour	O
,	O
with	O
a	O
finite	O
Curie	O
temperature	O
where	O
ferromagnetism	O
ceases	O
.	O
</s>
<s>
The	O
critical	O
behaviour	O
of	O
the	O
spherical	B-Algorithm
model	I-Algorithm
was	O
derived	O
in	O
the	O
completely	O
general	O
circumstances	O
that	O
the	O
dimension	O
d	O
may	O
be	O
a	O
real	O
non-integer	O
dimension	O
.	O
</s>
