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WORLD SCIENTIFIC eBooks

Critical Behavior of a Classical Heisenberg Ferromagnet with Many Degrees of Freedom

E. Brézin, D. J. Wallace

Published Aug 1, 1993• 2 citations
Publisher
DOI
10.1142/9789814365802_0002

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The critical behavior of a classical Heisenberg ferromagnet is studied in the limit where the spin dimensionality $N$ is large. Corrections of order $\frac{1}{N}$ to the spherical model are obtained as functions of a continuous dimension $d$, $2<d<4$. Particular attention is given to the behavior near the coexistence curve. The divergence of the magnetic susceptibility below ${T}_{c}$ as the external field vanishes is discussed through a nonlinear realization of the $O(N)$ symmetry, as well as in the $\frac{1}{N}$ and $4\ensuremath{-}d$ expansions.

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The critical behavior of a classical Heisenberg ferromagnet is studied in the limit where the spin dimensionality NNN is large. Corrections of order 1N\frac{1}{N}N1​ to the spherical model are obtained as functions of a continuous dimension ddd, 2<d<42<d<42<d<4. Particular attention is given to the behavior near the coexistence curve. The divergence of the magnetic susceptibility below Tc{T}_{c}Tc​ as the external field vanishes is discussed through a nonlinear realization of the O(N)O(N)O(N) symmetry, as well as in the 1N\frac{1}{N}N1​ and $4\ensuremath{-}d$ expansions.