Experimental Measurement of the Persistence Exponent of the Planar Ising Model

TL;DR

This study experimentally measures the persistence exponent in a planar Ising model using a liquid crystal system, confirming theoretical predictions with real-world data over a broad time scale.

Contribution

First experimental determination of the persistence exponent in a planar Ising model using liquid crystal dynamics, validating theoretical and simulation results.

Findings

Measured exponent $ heta = 0.19 \, \pm \, 0.031$

Scaling behavior observed from 0.4 to 200 seconds

Results agree with theoretical and numerical predictions

Abstract

Using a twisted nematic liquid crystal system exhibiting planar Ising model dynamics, we have measured the scaling exponent $\theta$ which characterizes the time evolution, $p(t) \sim t^{-\theta}$, 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, $\theta = 0.19 \pm 0.031$, in good agreement with theoretical analysis and numerical simulations.