  We explore the environment-induced synchronization phenomenon in two-level
systems in contact with a thermal dissipative environment. We first discuss the
conditions under which synchronization emerges between a pair of two-level
particles. That is, we analyze the impact of various model parameters on the
emergence of (anti-)synchronization such as the environment temperature, the
direct interaction between the particles, and the distance between them
controlling the collectivity of the dissipation. We then enlarge the system to
be composed of three two-level atoms to study the mutual synchronization
between different particle pairs. Remarkably, we observe in this case a rich
synchronization dynamics which stems from different possible spatial
configurations of the atoms. Particularly, in sharp contrast with the two-atom
case, we show that when the three atoms are in close proximity, appearance of
anti-synchronization can be obstructed across all particle pairs due to
frustration.
