We study the nonequilibrium stationary state (NESS) of the Ising model driven away from thermal equilibrium at temperature $T$ by a stochastic resetting protocol. This protocol, realizable via rapid quench of temperature and magnetic field, resets the magnetization to its fixed initial value $m_0$ at a constant rate $r$. In the resulting NESS, the magnetization acquires a nontrivial distribution, leading to a rich phase diagram in the $(T,r)$ plane. We establish these results exactly in one dimension and present scaling arguments supported by simulations in two dimensions. We show that this resetting protocol gives rise to a “pseudoferro” phase in the $(T,r)$ plane for $r>r^{*}\left(T\right)$ and $T>T_c$, where $r^{*}\left(T\right)$ is a crossover line separating the pseudoferro phase from a paramagnetic phase. This pseudoferro phase is characterized by a magnetization distribution that vanishes as $\sim m^{\zeta }$ as $m\to 0$, where $\zeta$ varies continuously with $T$ and $r$.

• Received 13 February 2020
• Accepted 28 May 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033182

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Published by the American Physical Society