Journal of Physics C Solid State Physics

The magnetically dilute XY ferromagnet. I. The quenched site case

J S Reeve, Donald D. Betts

Published Aug 21, 1975• 11 citations

Abstract

The spin- 1 / 2 XY model with quenched impurity sites is studied on three cubic lattices. Series of degree seven in inverse temperature at fixed magnetic-ion concentration and series of the same degree in magnetic-ion concentration at fixed temperature are generated for both the zero-field free energy and the zero-field fluctuation in the long-range order. The high-temperature series are too short for satisfactory analysis. The low-concentration series for the fluctuation however yield estimates for the critical exponent gamma , which appear to depend on temperature. The phase transition curve is estimated for all three lattices.

DOI: 10.1088/0022-3719/8/16/015

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Journal of Physics C Solid State Physics

The magnetically dilute XY ferromagnet. I. The quenched site case

J S Reeve, Donald D. Betts

Published Aug 21, 1975• 11 citations

Publisher

Abstract

DOI: 10.1088/0022-3719/8/16/015

Related papers

Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity

Olivia Mallick, Muktish Acharyya

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Donald D. Betts, R.V. Ditzian, C. J. Elliott +1 more

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Donald D. Betts, M. Howard Lee

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Physical Review LettersJun 24, 196835 citations

J(r)\propto r^{-n}

. We discuss the dependence of the critical temperature on the concentration of magnetic component and the index

n

for selected one-, two- and three-dimensional lattices.We confirm the absence of the critical concentration for a diluted magnet with infinite interaction range. In the regime of the low concentrations of magnetic component, we find a non-linear increase of the critical temperature with the concentration in the form of

T_{c}\propto p^{n/d}

, depending on the system dimensionality

d

and the index

n

, whereas

n > d

The

\mathrm{XY}

model of a quantum lattice fluid or a ferromagnet is studied by the method of exact high-temperature series expansion. Nine terms are obtained in the free-energy series and seven in the series for the square of the fluctuation in the long-range order. Analysis of these series yields the critical values $\frac{k{T}_{c}}{J}=4.84\ifmmode\pm\else\textpm\fi{}0.06$, $\ensuremath{\gamma}=1.00\ifmmode\pm\else\textpm\fi{}0.07$, and $\ensuremath{\alpha}=\ensuremath{-}0.20\ifmmode\pm\else\textpm\fi{}0.20$ for the fcc lattice.