<s>
In	O
mathematical	O
physics	O
,	O
a	O
lattice	B-Algorithm
model	I-Algorithm
is	O
a	O
mathematical	O
model	O
of	O
a	O
physical	O
system	O
that	O
is	O
defined	O
on	O
a	O
lattice	O
,	O
as	O
opposed	O
to	O
a	O
continuum	O
,	O
such	O
as	O
the	O
continuum	O
of	O
space	O
or	O
spacetime	B-Protocol
.	O
</s>
<s>
Lattice	B-Algorithm
models	I-Algorithm
originally	O
occurred	O
in	O
the	O
context	O
of	O
condensed	O
matter	O
physics	O
,	O
where	O
the	O
atoms	O
of	O
a	O
crystal	O
automatically	O
form	O
a	O
lattice	O
.	O
</s>
<s>
Currently	O
,	O
lattice	B-Algorithm
models	I-Algorithm
are	O
quite	O
popular	O
in	O
theoretical	O
physics	O
,	O
for	O
many	O
reasons	O
.	O
</s>
<s>
Lattice	B-Algorithm
models	I-Algorithm
are	O
also	O
ideal	O
for	O
study	O
by	O
the	O
methods	O
of	O
computational	B-Algorithm
physics	I-Algorithm
,	O
as	O
the	O
discretization	O
of	O
any	O
continuum	O
model	O
automatically	O
turns	O
it	O
into	O
a	O
lattice	B-Algorithm
model	I-Algorithm
.	O
</s>
<s>
Physical	O
lattice	B-Algorithm
models	I-Algorithm
frequently	O
occur	O
as	O
an	O
approximation	O
to	O
a	O
continuum	O
theory	O
,	O
either	O
to	O
give	O
an	O
ultraviolet	O
cutoff	O
to	O
the	O
theory	O
to	O
prevent	O
divergences	O
or	O
to	O
perform	O
numerical	B-General_Concept
computations	I-General_Concept
.	O
</s>
<s>
An	O
example	O
of	O
a	O
continuum	O
theory	O
that	O
is	O
widely	O
studied	O
by	O
lattice	B-Algorithm
models	I-Algorithm
is	O
the	O
QCD	O
lattice	B-Algorithm
model	I-Algorithm
,	O
a	O
discretization	O
of	O
quantum	O
chromodynamics	O
.	O
</s>
<s>
However	O
,	O
digital	B-General_Concept
physics	I-General_Concept
considers	O
nature	O
fundamentally	O
discrete	O
at	O
the	O
Planck	O
scale	O
,	O
which	O
imposes	O
upper	O
limit	O
to	O
the	O
density	O
of	O
information	O
,	O
aka	O
Holographic	O
principle	O
.	O
</s>
<s>
Lattice	B-Algorithm
models	I-Algorithm
are	O
also	O
used	O
to	O
simulate	O
the	O
structure	O
and	O
dynamics	O
of	O
polymers	O
.	O
</s>
<s>
A	O
number	O
of	O
lattice	B-Algorithm
models	I-Algorithm
can	O
be	O
described	O
by	O
the	O
following	O
data	O
:	O
</s>
<s>
In	O
the	O
limit	O
,	O
we	O
obtain	O
the	O
XY	B-Algorithm
model	I-Algorithm
which	O
has	O
.	O
</s>
<s>
Generalising	O
the	O
XY	B-Algorithm
model	I-Algorithm
to	O
higher	O
dimensions	O
gives	O
the	O
-vector	O
model	O
which	O
has	O
.	O
</s>
<s>
Suppose	O
the	O
continuum	B-Algorithm
limit	I-Algorithm
of	O
the	O
lattice	O
is	O
.	O
</s>
