The voter model and the Ising model are different physical systems. In the voter model, an agent copies a randomly chosen neighbor's opinion — the dynamics are interfacial, driven by noise at domain boundaries. In the Ising model, an agent flips based on energy minimization — the dynamics are curvature-driven, shrinking domains with high surface tension. The two models produce qualitatively different coarsening: voter dynamics generates rough interfaces with noise-dominated evolution; Ising dynamics generates smooth interfaces with curvature-dominated evolution.
Adding persistence — a confidence state where agents resist opinion change for some time after switching — transforms the voter model into the Ising universality class. The persistent voter model, with long-range interactions decaying as a power law with exponent α, belongs to the same universality class as the long-range Ising model quenched to low temperature. For all values of α.
The mechanism: persistence suppresses the interfacial noise that defines voter dynamics. An agent who recently changed opinion is temporarily frozen, unable to flip again immediately. This freezing eliminates the rapid back-and-forth at domain boundaries that generates the voter model's characteristic rough interfaces. With that noise suppressed, what remains is curvature-driven coarsening — the Ising mechanism emerges because the voter mechanism has been blocked.
Universality classes are determined not by the microscopic dynamics but by which fluctuations survive. Remove the characteristic fluctuation of one class, and the system falls into another. The persistent voter model doesn't interpolate between voter and Ising — it is Ising, once the noise that made it voter is gone.