Introduction

potts_hamiltonian(
    ig::LabelledGraphs.LabelledGraph{MetaGraphs.MetaGraph{Int64, T}} where T,
    num_states_cl::Int64;
    spectrum,
    cluster_assignment_rule
)

Create a Potts Hamiltonian.

This function constructs a Potts Hamiltonian from an Ising graph by introducing a natural order in Potts Hamiltonian coordinates.

Arguments:

• ig::IsingGraph: The Ising graph representing the spin system.
• num_states_cl::Int: The number of states per cluster taken into account when calculating the spectrum. In every cluster the number of states is constant.
• spectrum::Function: A function for calculating the spectrum of the Potts Hamiltonian. It can be full_spectrum or brute_force.
• cluster_assignment_rule::Dict{Int, L}: A dictionary specifying the assignment rule that maps Ising graph vertices to clusters. It can be super_square_lattice, pegasus_lattice or zephyr_lattice.

Returns:

• potts_h::LabelledGraph{S, T}: The Potts Hamiltonian represented as a labelled graph.

The potts_hamiltonian function takes an Ising graph (ig) as input and constructs a Potts Hamiltonian by introducing a natural order in Potts Hamiltonian coordinates. It allows you to specify the number of states per cluster, a spectrum calculation function, and a cluster assignment rule, which maps Ising graph vertices to clusters.

potts_hamiltonian(
    ig::LabelledGraphs.LabelledGraph{MetaGraphs.MetaGraph{Int64, T}} where T,
    num_states_cl::Dict{T, Int64};
    spectrum,
    cluster_assignment_rule
)

Create a Potts Hamiltonian.

This function constructs a Potts Hamiltonian from an Ising graph by introducing a natural order in Potts Hamiltonian coordinates.

Arguments:

• ig::IsingGraph: The Ising graph representing the spin system.
• num_states_cl::Dict{T, Int}: A dictionary specifying the number of states per cluster for different clusters. Number of states are considered when calculating the spectrum.
• spectrum::Function: A function for calculating the spectrum of the Potts Hamiltonian. It can be full_spectrum or brute_force.
• cluster_assignment_rule::Dict{Int, T}: A dictionary specifying the assignment rule that maps Ising graph vertices to clusters. It can be super_square_lattice, pegasus_lattice or zephyr_lattice.

Returns:

• potts_h::LabelledGraph{MetaDiGraph}: The Potts Hamiltonian represented as a labelled graph.

The potts_hamiltonian function takes an Ising graph (ig) as input and constructs a Potts Hamiltonian by introducing a natural order in Potts Hamiltonian coordinates. It allows you to specify the number of states per cluster which can vary for different clusters, a spectrum calculation function, and a cluster assignment rule, which maps Ising graph vertices to clusters.

potts_hamiltonian(
    ig::LabelledGraphs.LabelledGraph{MetaGraphs.MetaGraph{Int64, T}} where T;
    spectrum,
    cluster_assignment_rule
)

Create a Potts Hamiltonian with optional cluster sizes.

This function constructs a Potts Hamiltonian from an Ising graph by introducing a natural order in Potts Hamiltonian coordinates.

Arguments:

• ig::IsingGraph: The Ising graph representing the spin system.
• spectrum::Function: A function for calculating the spectrum of the Potts Hamiltonian. It can be full_spectrum or brute_force. Default is full_spectrum.
• cluster_assignment_rule::Dict{Int, T}: A dictionary specifying the assignment rule that maps Ising graph vertices to clusters. It can be super_square_lattice, pegasus_lattice or zephyr_lattice.

Returns:

• potts_h::LabelledGraph{MetaDiGraph}: The Potts Hamiltonian represented as a labelled graph.

The potts_hamiltonian function takes an Ising graph (ig) as input and constructs a Potts Hamiltonian by introducing a natural order in Potts Hamiltonian coordinates. You can optionally specify a spectrum calculation function and a cluster assignment rule, which maps Ising graph vertices to clusters. This version of potts_hamiltonian function does not truncate states in the cluster while calculating the spectrum. If you want to specify custom cluster sizes, use the alternative version of this function by passing a Dict{T, Int} containing the number of states per cluster as num_states_cl.