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

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.