  Relativistic magnetic turbulence has been proposed as a process for producing
nonthermal particles in high-energy astrophysics. The particle energization may
be contributed by both magnetic reconnection and turbulent fluctuations, but
their interplay is poorly understood. It has been suggested that during
magnetic reconnection the parallel electric field dominates the particle
acceleration up to the lower bound of the power-law particle spectrum, but
recent studies show that electric fields perpendicular to the magnetic field
can play an important, if not dominant role. In this study, we carry out fully
kinetic particle-in-cell simulations of magnetically dominated decaying
turbulence in a relativistic pair plasma. For a fixed magnetization parameter
$\sigma_0 = 20$, we find that the injection energy~$\varepsilon_{\rm inj}$
converges with increasing domain size to~$\varepsilon_{\rm inj} \simeq 10 \,
m_ec^2$. In contrast, the power-law index, the cut-off energy, and the
power-law extent increase steadily with domain size. We trace a large number of
particles and evaluate the contributions of the work done by the parallel
($W_\parallel$) and perpendicular ($W_\perp$) electric fields during both the
injection phase and the post-injection phase. We find that during the injection
phase, the $W_\perp$ contribution increases with domain size, suggesting that
it may eventually dominate injection for a sufficiently large domain. In
contrast, both components contribute equally during the post-injection phase,
insensitive to the domain size. For high energy ($\varepsilon \gg
\varepsilon_{\rm inj}$) particles, $W_\perp$ dominates the subsequent
energization. These findings may improve our understanding of nonthermal
particles and their emissions in astrophysical plasmas.
