Dynamic Response of Ising System to a Pulsed Field

TL;DR

This study investigates the dynamic response of the Ising model to pulsed magnetic fields using Monte Carlo simulations and meanfield theory, revealing critical divergences and peaks near transition temperatures.

Contribution

It provides a comparative analysis of Monte Carlo and meanfield approaches to understanding pulsed field effects on the Ising system, including finite size scaling and analytical solutions.

Findings

R_p diverges at T_c with exponent ~2.0

Pulse susceptibility  peaks near T_c^e, depending on pulse width

Meanfield results show divergence and peaks at transition temperature

Abstract

The dynamical response to a pulsed magnetic field has been studied here both using Monte Carlo simulation and by solving numerically the meanfield dynamical equation of motion for the Ising model. The ratio R_p of the response magnetisation half-width to the width of the external field pulse has been observed to diverge and pulse susceptibility \chi_p (ratio of the response magnetisation peak height and the pulse height) gives a peak near the order-disorder transition temperature T_c (for the unperturbed system). The Monte Carlo results for Ising system on square lattice show that R_p diverges at T_c, with the exponent $\nu z \cong 2.0$, while \chi_p shows a peak at $T_c^e$, which is a function of the field pulse width $\delta t$. A finite size (in time) scaling analysis shows that $T_c^e = T_c + C (\delta t)^{-1/x}$, with $x = \nu z \cong 2.0$. The meanfield results show that both the divergence of R and the peak in \chi_p occur at the meanfield transition temperature, while the peak height in $\chi_p \sim (\delta t)^y$, $y \cong 1$ for small values of $\delta t$. These results also compare well with an approximate analytical solution of the meanfield equation of motion.