Blume-Capel Model

The variables in the BlumeCapel model can take 3 values (spin-\(`1`\) as opposed to spin-\(`\frac12`\) in the Ising case).

\mathcal{H} = -\sum_{ij} J_{ij} s_{i}s_{j}\,,\quad s_i \in \{-1,0,+1\}

Hypergraph Generalization

The generalization is analogous to the Ising spin glass:

\mathcal{H} = -\sum_e J_e \prod_{i\in e} s_i

NOTE: Contrary to the Ising model, squared spin variables can be meaningful in the BlumeCapel model: \(`s_i\in\{-1,0,+1\}`\), \(`s_i^2\in\{0,1\}`\).

Example Input Data

{
  "type": "blume-capel",
  "version": "0.2",
  "terms": [
    {"c": 1.0, "ids": [0, 1]},
    {"c": 1.0, "ids": [1, 2]},
    {"c": 1.0, "ids": [2, 3]},
    {"c": -2.0, "ids": [3, 0]}
  ]
}