Zₙ Clock Model generalizes the Ising model to n discrete spin states: σ = e^{2πik/n}, k=0,…,n−1.
H = −J∑σᵢσⱼ† − h∑τᵢ where τ is the clock shift operator τ|k⟩=|k+1 mod n⟩.
Parafermions are Z_n generalizations of Majorana fermions, emerging at domain walls.
Left: clock spin chain with domain walls (parafermions). Right: phase diagram (J vs h) with ordered/disordered/critical phases.