The Visible Transition

Quantum phase transitions happen at zero temperature. Thermal fluctuations at any nonzero temperature wash out the sharp, non-analytic signatures that define a quantum critical point — the divergent correlation length, the power-law scaling, the universal exponents. Experimentalists work at millikelvin temperatures and extrapolate toward absolute zero. The transition itself is always, strictly, invisible.

Csepanyi et al. (arXiv:2602.00794) show it’s visible after all — not in static observables, but in dynamics. The order-parameter correlation time, measured within the causal light cone of the system’s excitations, retains non-analytic behavior at nonzero temperature. A new logarithmic divergence appears that is independent of temperature and continuously connects to the zero-temperature critical point.

The mechanism exploits a distinction between statics and dynamics. Static observables — magnetization, susceptibility, specific heat — are averaged over all configurations weighted by the Boltzmann distribution, which smooths non-analyticities at any T > 0. Dynamical observables — how correlations spread in time — are constrained by the light cone, which limits the configurations that contribute. The light cone acts as a filter: it selects the subset of excitations that propagate causally, and this subset retains the critical structure that the full thermal average destroys.

The logarithmic divergence is the specific signature. At the quantum critical point, the correlation time diverges logarithmically with system size inside the light cone, even at finite temperature. This divergence is absent away from the critical point. It provides a clean diagnostic: measure the dynamical correlation function, check for logarithmic scaling with system size, and the presence or absence of the divergence tells you whether the system is at (or near) the quantum critical point — all at experimental temperatures.

The structural insight: the information about the quantum phase transition was always present at finite temperature. It wasn’t destroyed by thermal fluctuations — it was hidden in the dynamics, encoded in the time-dependent structure of correlations rather than in their static averages. Statics said the transition was invisible. Dynamics says it’s been there all along.

Csepanyi et al., “Observing quantum phase transitions at non-zero temperature,” arXiv:2602.00794 (2026).