2007 journal article
Integral equation procedure based on tailored orthogonal functions for the XY spin fluid in an external magnetic field
PHYSICAL REVIEW E, 76(4).
TL;DR:
This work uses numerical simulations and integral equation techniques to study a system that is anisotropic in the azimuthal angle phi, producing in the latter case a formalism that is identical to that of the simpler isotropic version having no external field.
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Added: August 6, 2018
The classical XY model describes particles in three-dimensional space that carry magnetic moments or spins whose motion is restricted to rotations in a plane. Introduction of an external magnetic field lying in the same plane then generates a system that is anisotropic in the azimuthal angle phi . We use numerical simulations and integral equation techniques to study this system, producing in the latter case a formalism that is identical to that of the simpler isotropic version having no external field. The basis for this simplification is a generalization Em(phi) of the ordinary exponential basis set eimphi that restores orthogonality in the presence of the external field. We display results of sample calculations obtained with two integral equation closures, reference hypernetted-chain and soft mean-spherical approximation, both coupled to the Lovett-Mou-Buff-Wertheim relation, along with results from the numerical simulations for comparison. Construction of the Em(phi) is described in an Appendix.