Experimental Measurement of the Persistence Exponent of the Planar Ising Model

Abstract

Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent $θ$ which characterizes the time evolution, $p(t) \sim t^{-θ}$, of the probability p(t) that the local order parameter has not switched its state by the time t. For 0.4 seconds to 200 seconds following the phase quench, the system exhibits scaling behavior and, measured over this interval, $θ= 0.19 \pm 0.031$, in good agreement with theoretical analysis and numerical simulations.