- #1
jfy4
- 649
- 3
While reading through Kogut's lattice gauge theory introduction he goes through the area and perimeter laws for lattice gauge models. The result is something like this
[tex]
\left\langle \prod _{l\in C}\sigma_{3}(l) \right\rangle \sim \exp(-P)
[/tex]
for low temperature, and
[tex]
\left\langle \prod _{l\in C}\sigma_{3}(l) \right\rangle \sim \exp(-A)
[/tex]
for high temperature. He then says
[tex]
\left\langle \prod _{l\in C}\sigma_{3}(l) \right\rangle \sim \exp(-P)
[/tex]
for low temperature, and
[tex]
\left\langle \prod _{l\in C}\sigma_{3}(l) \right\rangle \sim \exp(-A)
[/tex]
for high temperature. He then says
However, I can certainly conceive of a couple different closed loops which have more perimeter units than area units. Is this relationship between area size and perimeter size more subtle, or have I missed something. Thanks.So, at high T the correlation function falls very quickly as the loop is taken larger and larger, while at low T it falls off at a qualitatively slower rate.