Arc-shaped structure factor in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mtext>−</mml:mtext><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mtext>−</mml:mtext><mml:msub><mml:mi>J</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> classical Heisenberg model on the triangular lattice
Cecilie Glittum, Olav F. Syljuåsen
Abstract
We study the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ classical Heisenberg model with ferromagnetic ${J}_{1}$ on the triangular lattice using the nematic bond theory. For parameters where the momentum space coupling function ${J}_{\stackrel{P\vec}{q}}$ shows a discrete set of minima, we find that the system in general exhibits a single first-order phase transition between the high-temperature ring liquid and the low-temperature single-$\stackrel{P\vec}{q}$ planar spiral state. Close to where ${J}_{\stackrel{P\vec}{q}}$ shows a continuous minimum, we on the other hand find several phase transitions upon lowering the temperature. Most interestingly, we find an intermediate temperature ``arc'' regime, where the structure factor breaks rotational symmetry and shows a broad arc-shaped maximum. We map out the parameter region over which this arc regime exists and characterize details of its static structure factor over the same region.