Critical dynamics and phase transition of a strongly interacting warm spin gas



Research into new phases of matter and, in general, the investigation of correlated states of many particles are at the limit of interdisciplinary physical research. Ordered phases are examined in detail in condensed matter and in atomic physics, especially in low-temperature spin systems. At ambient temperature, however, spin gases are considered to be disordered, with high entropy and weak or random many-body interactions. In this work we discover a new magnetic phase of cesium vapor at room temperature. In the vicinity of the phase boundary we observe a 100-fold increase in the reaction time of the spins. Our results open up exciting ways to precise quantum sensors, to magnetic imbalance simulations with many-particle correlations and to the realization of Ising calculations under ambient conditions.


Phase transitions are emergent phenomena in which microscopic interactions drive a disordered system into a collectively ordered phase. The system can show critical, scale-invariant behavior near the boundary between two phases. Here we report a second-order phase transition accompanied by critical behavior in a system of warm cesium spins driven by linearly polarized light. The ordered phase exhibits macroscopic magnetization when the interactions between the spins become dominant. We measure the phase diagram of the system and observe the collective behavior near the phase boundaries, including the power law dependence of magnetization and the divergence of susceptibility. Outside of equilibrium, we observe a critical two orders of magnitude slowdown in the spin reaction time, which exceeds 5 s near the phase boundary. This work creates a controlled platform for the investigation of equilibrium and non-equilibrium properties of magnetic phases.


    • Accepted 17.09.2021.
  • Author contributions: YH, OK, OR and OF designed the research; YH and OK did research; YH contributed new reagents / analysis tools; YH analyzed data; and YH, OK, OR and OF wrote the work.

  • The authors do not declare any competing interests.

  • This article is a PNAS direct submission.

  • Released under the PNAS license.

  • This article provides supporting information online at

Data availability

All study data are included in this article and / or SI appendix.


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