  Power-law exponents in the convergence to effective ergodicity is quantified
for Ising-Lenz model in one dimension. Modified Thirumalai-Mountain (TM) metric
for magnetisation is computed for the range of temperature values under
strongly correlated dynamics. In producing evolution of TM metric over time,
time-averaged dynamics is generated by using Metropolis and Glauber
single-spin-flip dynamics, and ensemble-averaged dynamics with an exact
solution. Superdiffusive behaviour is numerically identified in the parameter
regimes studied, i.e., power-law exponents, $\alpha > 1.0$.
