  In the transition metal dichalcogenide IrTe$_2$, low-temperature
charge-ordered phase transitions involving Ir dimers lead to the occurrence of
stripe phases of different periodicities, and nearly degenerate energies.
Bulk-sensitive measurements have shown that, upon cooling, IrTe$_2$ undergoes
two such first-order transitions to $(5\times1\times5)$ and $(8\times1\times8)$
reconstructed phases at $T_{c_1}\sim 280$~K and $T_{c_2}\sim 180$~K,
respectively. Here, using surface sensitive probes of the electronic structure
of IrTe$_2$, we reveal the first-order phase transition at $T_{c_3}=165$~K to
the $(6\times1)$ stripes phase, previously proposed to be the surface ground
state. This is achieved by combining x-ray photoemission spectroscopy and
angle-resolved photoemission spectroscopy, which give access to the evolution
of stripe domains and a particular surface state, the energy of which is
dependent on the Ir dimer length. By performing measurements over a full
thermal cycle, we also report the complete hysteresis of all these phases.
