Phenomenological Dynamics of Ising Magnets in the Presence of Magnetic Field: Widom Lines Captured from Slow Relaxation Time

Abstract

A complete phenomenological description for the relaxation dynamics of the Ising ferromagnets in the presence of external magnetic field h is given by using the pair approximation. To study the relaxation dynamics, we calculate two characteristic times (denoted as τS, τF ) using the rate constants which satisfy the Onsager reciprocity theorem. Temperature/magnetic field variations of τS and τF are investigated. We have shown that the extrema of the curves obtained for τS when h 6= 0 determine the loci of correlation length maxima or the Widom lines. The results are compared with those of response functions and thermodynamic curvature. We observe that they exactly match that for the magnetic susceptibility.