\(
%Residues
\let\Res\relax
\DeclareMathOperator*{\Res}{Res}
%Allow us to write angstroms
\let\ring\r
\renewcommand{\r}{\textbf{r}}
\let\Oersted\O
\let\O\relax
\DeclareMathOperator{\O}{O}
%Define useful symbols for commonly used sets in mathematics
\newcommand{\NN}{\mathbb{N}}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\TT}{\mathbb{T}}
%\newcommand{\H}{\mathbb{H}}
%Useful symbols for differential geometry
\newcommand{\M}{\mathcal{M}}
\renewcommand{\d}{\text{d}}
\newcommand{\Sphere}{\mathbb{S}}
\newcommand{\Torus}{\mathbb{T}}
%Useful notations for electromagnetism
\newcommand{\E}{\mathbf{E}}
\newcommand{\B}{\mathbf{B}}
\newcommand{\A}{\mathbf{A}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\J}{\mathbf{J}}
\newcommand{\R}{\boldsymbol{R}}
%Useful symbols for vector notation
\newcommand{\x}{\boldsymbol{x}}
\newcommand{\y}{\boldsymbol{y}}
\newcommand{\z}{\boldsymbol{z}}
\newcommand{\p}{\boldsymbol{p}}
\newcommand{\q}{\boldsymbol{q}}
\newcommand{\w}{\boldsymbol{w}}
\renewcommand{\k}{\boldsymbol{k}}
\newcommand{\K}{\boldsymbol{K}}
\newcommand{\Q}{\boldsymbol{Q}}
\renewcommand{\r}{\boldsymbol{r}}
%Useful symbols for physics
\newcommand{\hc}{\text{H.c.}}
\newcommand{\Hc}{\text{H.c.}}
\newcommand{\BZ}{\text{BZ}}
\newcommand{\Kn}{\text{Kn}}
\newcommand{\g}{\mathfrak{g}}
\newcommand{\ahat}{\hat{a}}
\newcommand{\bhat}{\hat{b}}
\newcommand{\chat}{\hat{c}}
\newcommand{\dhat}{\hat{d}}
\newcommand{\ehat}{\hat{e}}
\newcommand{\fhat}{\hat{f}}
\newcommand{\ghat}{\hat{g}}
\newcommand{\hhat}{\hat{h}}
\newcommand{\ihat}{\hat{i}}
\newcommand{\jhat}{\hat{j}}
\newcommand{\khat}{\hat{k}}
\newcommand{\lhat}{\hat{l}}
\newcommand{\mhat}{\hat{m}}
\newcommand{\nhat}{\hat{n}}
\newcommand{\ohat}{\hat{o}}
\newcommand{\phat}{\hat{p}}
\newcommand{\qhat}{\hat{q}}
\newcommand{\rhat}{\hat{r}}
\newcommand{\shat}{\hat{s}}
\newcommand{\that}{\hat{t}}
\newcommand{\uhat}{\hat{u}}
\newcommand{\vhat}{\hat{v}}
\newcommand{\what}{\hat{w}}
\newcommand{\xhat}{\hat{x}}
\newcommand{\yhat}{\hat{y}}
\newcommand{\zhat}{\hat{z}}
\newcommand{\Ahat}{\hat{A}}
\newcommand{\Bhat}{\hat{B}}
\newcommand{\Chat}{\hat{C}}
\newcommand{\Dhat}{\hat{D}}
\newcommand{\Ehat}{\hat{E}}
\newcommand{\Fhat}{\hat{F}}
\newcommand{\Ghat}{\hat{G}}
\newcommand{\Hhat}{\hat{H}}
\newcommand{\Ihat}{\hat{I}}
\newcommand{\Jhat}{\hat{J}}
\newcommand{\Khat}{\hat{K}}
\newcommand{\Lhat}{\hat{L}}
\newcommand{\Mhat}{\hat{M}}
\newcommand{\Nhat}{\hat{N}}
\newcommand{\Ohat}{\hat{O}}
\newcommand{\Phat}{\hat{P}}
\newcommand{\Qhat}{\hat{Q}}
\newcommand{\Rhat}{\hat{R}}
\newcommand{\Shat}{\hat{S}}
\newcommand{\That}{\hat{T}}
\newcommand{\Uhat}{\hat{U}}
\newcommand{\Vhat}{\hat{V}}
\newcommand{\What}{\hat{W}}
\newcommand{\Xhat}{\hat{X}}
\newcommand{\Yhat}{\hat{Y}}
\newcommand{\Zhat}{\hat{Z}}
\newcommand{\HH}{\mathcal{H}}
\newcommand{\Pihat}{\hat{\Pi}}
\newcommand{\sigmahat}{\hat{\sigma}}
\newcommand{\psihat}{\hat{\psi}}
\newcommand{\Psihat}{\hat{\Psi}}
\newcommand{\phihat}{\hat{\phi}}
\newcommand{\thetahat}{\hat{\theta}}
\newcommand{\Thetahat}{\hat{\Theta}}
\newcommand{\chihat}{\hat{\chi}}
\newcommand{\Phihat}{\hat{\Phi}}
\newcommand{\Omegahat}{\hat{\Omega}}
\newcommand{\Deltahat}{\hat{\Delta}}
\newcommand{\pihat}{\hat{\pi}}
\newcommand{\varphihat}{\hat{\varphi}}
\newcommand{\rhohat}{\hat{\rho}}
\newcommand{\gammahat}{\hat{\gamma}}
\newcommand{\etahat}{\hat{\eta}}
\newcommand{\V}{\mathcal{V}}
\renewcommand{\L}{\mathcal{L}}
\newcommand{\D}{\mathcal{D}}
\newcommand{\id}{\text{id}}
\DeclareMathOperator{\Vol}{Vol}
\DeclareMathOperator{\atan}{atan}
\DeclareMathOperator{\Tr}{Tr}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\conv}{conv}
\DeclareMathOperator{\preim}{preim}
\DeclareMathOperator{\proj}{proj}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\ver}{ver}
\DeclareMathOperator{\hor}{hor}
\DeclareMathOperator{\ad}{ad}
\DeclareMathOperator{\const}{const}
\DeclareMathOperator{\Ad}{Ad}
\DeclareMathOperator{\SU}{SU}
\DeclareMathOperator{\Cl}{C\ell}
\DeclareMathOperator{\conf}{conf}
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\algsl}{\mathfrak{sl}}
\DeclareMathOperator{\Sp}{Sp}
\DeclareMathOperator{\algsu}{\mathfrak{su}}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Unit}{U}
\DeclareMathOperator{\algu}{\mathfrak{u}}
\DeclareMathOperator{\SO}{SO}
\DeclareMathOperator{\algso}{\mathfrak{so}}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\erfc}{erfc}
\DeclareMathOperator{\Log}{Log}
\DeclareMathOperator{\arccot}{arccot}
\DeclareMathOperator{\arccsc}{arccsc}
\DeclareMathOperator{\arcsec}{arcsec}
\DeclareMathOperator{\artanh}{artanh}
\DeclareMathOperator{\arsinh}{arsinh}
\DeclareMathOperator{\arcosh}{arcosh}
\DeclareMathOperator{\arcoth}{arcoth}
\DeclareMathOperator{\arcsch}{arcsch}
\DeclareMathOperator{\arsech}{arsech}
\DeclareMathOperator{\sech}{sech}
\DeclareMathOperator{\csch}{csch}
\DeclareMathOperator{\Alt}{Alt}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Arg}{Arg}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Spin}{Spin}
\DeclareMathOperator{\Diff}{Diff}
\DeclareMathOperator{\Der}{Der}
\DeclareMathOperator{\Witt}{Witt}
\DeclareMathOperator{\Vir}{Vir}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\Pf}{Pf}
\DeclareMathOperator{\Li}{Li}
\DeclareMathOperator{\vecspan}{span}
\DeclareMathOperator{\dist}{dist}
\DeclareMathOperator{\dom}{dom}
\DeclareMathOperator{\range}{range}
\DeclareMathOperator{\1}{\mathbb{1}}
\DeclareMathOperator{\Ai}{Ai}
\DeclareMathOperator{\Bi}{Bi}
\let\Re\relax
\DeclareMathOperator{\Re}{Re}
\let\Im\relax
\DeclareMathOperator{\Im}{Im}
%Useful notations for thermodynamics
\newcommand{\dbar}}
\)
\(\require{cancel}\)
\(\require{simpler-wick}\)
\(\require{braket}\)
-
Write down the form of the next term in the expansion, which couples four spins together.