EDIT: Previous section of the question for context: The Ising model currently used in electromagnetism, statistical mechanics, as well as image processing is associated with the state space $$S = (−1, +1)^E$$ I'm currently working on an assignment and one of the questions contains the following statement.
$$E = \{1, . . . , L\} \times \{1, . . . , L\}.$$
The lattice $E$ is equipped with the following graph structure:
$$j_1 = (i_1, i_2 + 1)$$ $$j_2 = (i_1 + 1, i_2)$$ $$j_3 = (i_1, i_2 − 1)$$ and $$j_4 = (i_1 − 1, i_2).$$
EDIT:around some state$$ (i_1, i_2) ∈ E.$$Two neighbors $$i, j ∈ E$$ are denoted by $$i ∼ i'$$
Does anyone know what the graph looks like or how to interpret it?
Cheers