= Solution
{c}
Above the transition, $\epsilon=0$ and both site types have the same <g-factor> $g$. For the given spin-only Zeeman Hamiltonian, adjacent $S=1$ levels have the same energy spacing, so fixed-frequency <electron paramagnetic resonance> gives a single resonance field $B_0=h\nu/(g\mu_B)$, ignoring unresolved additional interactions.
Below the transition, half the elongation axes lie along $x$ and half along $y$. A field along $x$ is parallel to the long bond on one sublattice and perpendicular on the other. The line splits into
$$
\boxed{B_\parallel=\frac{h\nu}{\mu_B(g+\epsilon/\gamma)}<B_0,\qquad B_\perp=\frac{h\nu}{\mu_B(g-\epsilon/\delta)}>B_0.}
$$
The separation grows on cooling as the distortion grows. Equal site populations give comparable integrated weights when the microwave coupling to the two sites is equivalent; populations alone do not fix all polarization-dependent intensities.
A suitable staggered structural <order parameter> is
$$
\Psi=\frac12[(l_x-l_y)_A-(l_x-l_y)_B].
$$
For an $x$-elongated A site and a $y$-elongated B site, $\Psi=\epsilon$, with the opposite sign for the domain interchanging the pattern. The <electron paramagnetic resonance> data determine its magnitude from
$$
\boxed{|\Psi|=\frac{(h\nu/\mu_B)(B_\parallel^{-1}-B_\perp^{-1})}{\gamma^{-1}+\delta^{-1}}.}
$$
For small splitting this is equivalently proportional to $B_\perp-B_\parallel$, but the reciprocal-field formula follows directly from the stated <g-factors>. It does not fix the sign of the structural domain. In a continuous transition $|\Psi|$ tends continuously to zero at $T_{\mathrm{JT}}$ and grows below it, eventually saturating. A mean-field sketch has $|\Psi|\propto(T_{\mathrm{JT}}-T)^{1/2}$ close to the transition; continuity alone does not determine that exponent. The last panel of the original orbital figure shows this illustrative behavior.
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