Evidence of invariance of time scale at critical point in the Ising meanfield equilibrium equation of state

TL;DR

This study numerically investigates the critical slowing down in the meanfield Ising model, demonstrating the invariance of the time scale at the critical point through divergence in iteration counts and comparing results with analytic and experimental data.

Contribution

It provides numerical evidence of the invariance of the time scale at the critical point in the meanfield Ising model, linking critical slowing down to the equilibrium equation of state.

Findings

Iteration count diverges as temperature approaches critical point

Estimated critical exponent matches analytic predictions

Numerical results agree with experimental observations

Abstract

We solved the equilibrium meanfield equation of state of Ising ferromagnet (obtained from Bragg-Williams theory) by Newton-Raphson method. The number of iterations required to get a convergent solution (within a specified accuracy) of equilibrium magnetisation, at any particular temperature, is observed to diverge in a power law fashion as the temperature approaches the critical value. This was identified as the critical slowing down. The exponent is also estimated. This value of the exponent is compared with that obtained from analytic solution. Besides this, the numerical results are also compared with some experimental results exhibiting satisfactory degree of agreement. It is observed from this study that the information of the invariance of time scale at the critical point is present in the meanfield equilibrium equation of state of Ising ferromagnet.