Susceptibilities and Correlation Functions of the Anisotropic Spherical Model

TL;DR

This paper calculates the static correlation functions of an exactly solvable anisotropic spherical model, revealing unique behaviors in the ordered phase and differences from the standard spherical model.

Contribution

It provides exact solutions for correlation functions in the anisotropic spherical model, highlighting differences from the classical spherical model and analyzing spin-wave effects.

Findings

Transverse correlation function follows Ornstein-Zernike form at small wave vectors.

Longitudinal correlation function exhibits nontrivial behavior due to spin-wave fluctuations.

In the isotropic case below T_c, S_{zz}(k) rac{1}{k} for small k.

Abstract

The static transverse and longitudinal correlation functions (CF) of a 3-dimensional ferromagnet are calculated for the exactly solvable anisotropic spherical model (ASM) determined as the limit D \to \infty of the classical D-component vector model. The results are nonequivalent to those for the standard spherical model of Berlin and Kac even in the isotropic case. Whereas the transverse CF has the usual Ornstein-Zernike form for small wave vectors, the longitudinal CF shows a nontrivial behavior in the ordered region caused by spin-wave fluctuations. In particular, in the isotropic case below T_c one has S_{zz}(k) \propto 1/k (the result of the spin-wave theory) for k \lsim \kappa_m \propto T_c-T.