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JYU Condensed Matter Theory
usadelndsoc
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c4fbae73
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c4fbae73
authored
2 years ago
by
patavirt
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doc/discretization.md
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...
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@@ -184,7 +184,7 @@ permutations.
## Matrix current
We can also calculate the matrix current $j
\m
apsto{}i$ between neighboring cells:
We can also calculate the matrix current $
`
j\mapsto{}i
`
$ between neighboring cells:
```
math
J_{ij}^a
=
...
...
@@ -223,7 +223,7 @@ $`\mathcal{O}(h^2)`$. The asymmetry arises when $`T^a`$ does not commute
with $
`U_{ij}`
$, so it is an issue only for the SU(2) component. The
problem is only in the interpretation.
The currents measured at sites
$
`i`
$ and $
`j`
$
are different: since
The currents measured at sites
*i*
and
*j*
are different: since
the parallel transport of spin between these two locations can imply
rotation due to the gauge field, there's no reason why we should have
$
`J_{ij}=-J_{ji}`
$, except in the continuum limit where the two points
...
...
@@ -239,5 +239,5 @@ automatic differentiation (AD). Only a routine evaluating the value of
the action is then needed, in terms of the AD dual variables.
When looking for the saddle point in equilibrium, the problem becomes
even simpler;
$
`Q`
$
has then additional restrictions, and we are looking
for the minimum of the free energy
$
`S`
$
.
even simpler;
*Q*
has then additional restrictions, and we are looking
for the minimum of the free energy
*S*
.
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