Add info about approximations in phi4 docstrings (#165)

* add information about the approximations in phi4real docstring

* bump

* add phi4_complex

Author: VictorVanthilt

Project.toml

@@ -1,6 +1,6 @@
 name = "TNRKit"
 uuid = "7dfc3ef0-df9b-475f-b8e2-b91f34f5d84d"
-version = "0.5.0"
+version = "0.5.1"
 authors = ["Victor Vanthilt, Adwait Naravane, Atsushi Ueda and contributors"]
 
 [deps]

src/models/phi4_complex.jl

@@ -156,10 +156,23 @@ Compatible with no symmetry, explicit ℤ₂×ℤ₂ symmetry or explicit U(1) s
 Defaults to U(1) symmetry if the symmetry type is not provided.
 
 ### Arguments
-- `K::Integer`: Number of quadrature points for Gauss-Hermite integration.
+- `K::Integer`: Approximation parameter.
 - `μ0::Float64`: Bare mass. Note that in the calculation actually ``µ_0^2`` is used, but for readibility we write the ``µ_0^2`` as μ0
 - `λ::Float64`: Coupling constant.
 
+### Approximation parameter `K`
+#### Trivial (no symmetry)
+The tensor is constructed by performing a Gauss-Hermite quadrature to approximate the integrals in the partition function.
+The bond dimension is equal to `K^2`.
+
+#### ℤ₂×ℤ₂ symmetry
+The tensor is constructed by Taylor expanding the mixed sites term in the partition function.
+The order of the Taylor expansion is `K`. The total bond dimension is `K^2`.
+
+#### U(1) symmetry
+The tensor is constructed by Taylor expanding the mixed sites term in the partition function.
+The order of the Taylor expansion is `K`. The total bond dimension is `K^2`.
+
 ### Examples
 ```julia
     phi4_complex(10, -1., 1.)

src/models/phi4_real.jl

@@ -49,17 +49,24 @@ Constructs the partition function tensor for a 2D square lattice
 for the real ϕ^4 model with a given approximation (and bond dimension) `K`, bare mass ``µ_0^2`` `μ0`, interaction constant `λ` and external field `h`.
 
 Compatible with no symmetry or with explicit ℤ₂ symmetry on each of its spaces.
-The latter is based on Taylor expanding the mixed sites term, and requires the external field `h` to be zero.
 Defaults to ℤ₂ symmetry and `h = 0` if the symmetry type and magnetic field are not provided.
 
-It is based on [Gauss-Hermite quadrature](https://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature).
-
 ### Arguments
-- `K::Integer`: Number of quadrature points for Gauss-Hermite integration. Has to be even for the ℤ₂ symmetric version.
+- `K::Integer`: Approximation parameter.
 - `μ0::Float64`: Bare mass. Note that in the calculation actually ``µ_0^2`` is used, but for readibility we write the ``µ_0^2`` as μ0
 - `λ::Float64`: Coupling constant.
 - `h::Float64`: External field (default is 0).
 
+### Approximation parameter `K`
+#### Trivial (no symmetry)
+The tensor is constructed by performing a Gauss-Hermite quadrature to approximate the integrals in the partition function.
+The bond dimension is equal to the number of quadrature points `K`.
+
+#### ℤ₂ symmetry
+The tensor is constructed by Taylor expanding the mixed sites term in the partition function.
+The order of the Taylor expansion is K, and the bond dimension is K/2 for the even and odd sectors each (K in total).
+Not compatible with a non-zero magnetic field, as the magnetic field breaks the ℤ₂ symmetry.
+
 ### Examples
 ```julia
     phi4_real(10, -1.0, 1.0, 1.0) # default ℤ₂ symmetry, h = 0