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Active Spherical Model

The spherical model is a popular solvable model and has been applied to describe several critical phenomena such as the ferromagnetic transition, Bose-Einstein condensation, spin-glass transition, glass transition, jamming transition, and so on. Motivated by recent developments of active matter, here we consider the spherical model driven by the Ornstein-Uhlenbeck type self-propulsion force with persistent time $τ_p$. We show that the model exhibits the Ising universality for finite $τ_p$. On the contrary, the model exhibits the random field Ising universality in the limit $τ_p\to\infty$.