# Experimental realization of directed percolation criticality in turbulent liquid crystals

## TL;DR

This paper reports the first clear experimental realization of directed percolation criticality in turbulent liquid crystals, demonstrating static and dynamic critical behavior consistent with the DP universality class in 2+1 dimensions.

## Contribution

The authors develop an experimental method to observe DP criticality in turbulent liquid crystals, confirming key theoretical predictions including rapidity symmetry.

## Key findings

- Measured 12 critical exponents matching DP class
- Confirmed rapidity symmetry experimentally
- Demonstrated DP universality in a new out-of-equilibrium system

## Abstract

This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A. Takeuchi et al., Phys. Rev. Lett. 99, 234503 (2007)]. We further investigate both static and dynamic critical behavior of this phase transition, measuring a total of 12 critical exponents, 5 scaling functions, and 8 scaling relations, all in full agreement with those characterizing the DP class in 2+1 dimensions. Developing an experimental technique to create a seed of topological-defect turbulence by pulse laser, we confirm in particular the rapidity symmetry, which is a basic but nontrivial consequence of the field-theoretic approach to DP. This provides the first clear experimental realization of this outstanding, truly out-of-equilibrium universality class, dominating most phase transitions into an absorbing state.