Magnetic Phase Boundary of the Spin-½ Heisenberg Ferromagnetic Model

Abstract

We compute in this paper the exact coefficients, in a magnetic field, of the first eight powers of $x=\frac{J}{\ensuremath{\kappa}T}$ for the spin-\textonehalf{} Heisenberg ferromagnetic model for five lattices. We use this result to obtain the magnetic equation of state in the form $tanh(\frac{H}{\ensuremath{\kappa}T})=Mg(x,{M}^{2})$; again we obtain the exact coefficients for the first eight powers of $x$. From this equation, we are able to extrapolate and determine the magnetic phase houndary with reasonable accuracy for $M<0.8$. We have investigated the critical exponents $\mathbf{\ensuremath{\iota}}$, $\ensuremath{\beta}$, and $\ensuremath{\delta}$. We are unable to determine $\mathbf{\ensuremath{\iota}}$; we find an effective $\ensuremath{\beta}$ over a range of $M$ of $\ensuremath{\beta}=0.35\ifmmode\pm\else\textpm\fi{}0.05$, and we estimate $\ensuremath{\delta}=5.0\ifmmode\pm\else\textpm\fi{}0.2$.