Ising Model

Hamiltonian

The famous Hamiltonian of the Ising model is given by

\begin{align} \mathcal{H} = -\sum{\langle i,j \rangle} \sigmai \sigma_j , \end{align}

where $\langle i, j \rangle$ indicates that the sum has to be taken over nearest neighbors.

You can create an Ising model as follows,

model = IsingModel(; dims::Int=2, L::Int=8)

The following parameters can be set via keyword arguments:

dims: dimensionality of the cubic lattice (i.e. 1 = chain, 2 = square lattice, etc.)
L: linear system size

You can find example simulations of the 2D Ising model under Getting started and here: 2D Ising model.

Famous Ising model on a cubic lattice.

IsingModel(; dims, L)

Create Ising model on dims-dimensional cubic lattice with linear system size L.

IsingModel(params::Dict)
IsingModel(params::NamedTuple)

Create an Ising model with (keyword) parameters as specified in the dictionary/named tuple params.

The model can be solved exactly by transfer matrix method (Onsager solution). This gives the following results.

Critical temperature: $T_c = \frac{2}{\ln{1+\sqrt{2}}}$

Magnetization (per site): $m = \left(1-\left[\sinh 2\beta \right]^{-4}\right)^{\frac {1}{8}}$

Pull requests are very much welcome!