# PottsGauge

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Gauge transforms over the pair of Hamiltonian Potts parameters `(J,h)`

. Assuming we have
a vector `x`

of length `N`

, and `x[i] ∈ 1:q`

(`q`

state Potts variable), a gauge transform
is a change `(J,h)→(J',h')`

such that for all Potts configurations `x`

`E(x,J,h)-E(x,J',h')=const`

.

The module defines the gauge-transforms `gauge`

of pair `J,h`

. `J,h`

are arrays of size `q×q×N×N, q×N`

respectively. `J`

should be symmetric: `J[a,b,i,j] == J[b,a,j,i]`

; if this is not the case it throws an error. Allowed `gauge`

are: `ZeroSumGauge,LatticeGas,WildType,ExternalGauge`

.

```
Usage:
gauge(J,h,ZeroSumGauge())
gauge(J,h,Wildtype(x0))
gauge(J,h,ExternalGauge(U,V,C))
where:
* For `WildType` `x0` is a `Vector{Int}` of size `N` whose values are in the interval `1,…,q`
* For `ExternalGauge`, `U`,`V` are `q×N×N` arrays, and C is vector of length `N`.
```