How to Stabilize the Unstable: The Formula of Hidden Phases express

Original: "Tracking metastable phases by complex Lee-Yang zeros"
arXiv:2606.08004 · 2026-06-06 · CC BY 4.0 · 1 min
Metastable states of matter can be stabilized by vibration — scientists have found a mathematical key to hidden phases.

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Imagine a slide with three dips: the deepest one is a stable position for a ball, the middle one is precarious. A slight push and the ball rolls down. Yet, constant vibration of the right strength can hold it in the middle hollow for a long time.

In the 1950s, physicists Lee and Yang discovered that all states of matter are separated by invisible points in the world of imaginary numbers. These points, called Lee-Yang zeros, outline the phases. Stable phases are tucked far away, while shaky (metastable) ones creep up to the real axis. Research has shown: vibration shifts these zeros, and the shaky state becomes stable. The stronger the forcing, the more real the hidden phase becomes.

Supercooled water remains liquid even at –40°C — a precarious equilibrium shattered by the tiniest dust particle.

Terahertz light pulses act like that very 'shaking', only electromagnetic. By controlling light, we can program material properties. The most surprising part: the distance from a Lee-Yang zero to the real axis precisely determines the required vibration intensity. Entropy of the system behaves like a coordinate on an imaginary map, and spectroscopy becomes a control panel.

Supercooled water in clouds can stay liquid even at –40°C until it meets a dust particle or a shock wave.

In Peter Watts' novel 'Blindsight', the characters encounter metastable states of consciousness — almost like a shaky phase of matter.

Scientists
Ludwig BoltzmannRudolf ClausiusNiels BohrPascual JordanWerner HeisenbergJacob Bekenstein
Concepts
phase diagram Yang-Mills equation metastable state magnetic field lines landau level ising model magnetic state Dynamical Systems energy landscape London equations false vacuum non equilibrium state time crystals