  We focus on three-component SU(3) Fermi gases loaded into a square optical
lattice, with population imbalance between one component and the others. At
strong coupling the system is described by the SU(3) Heisenberg model with an
external field that couples to the population imbalance. We discuss the ground
state at the mean-field level and then analyze the thermal fluctuations with
the semi-classical Monte Carlo method. The interplay of interactions,
population imbalance and thermal fluctuations gives rise to a phase transition
linked to the breaking of an emergent Ising symmetry, despite the absence of
frustration. This represents a new scenario of discrete symmetry breaking in
low-dimensional systems with continuous symmetries. Possible implementations
with cold alkaline-earth(-like) atoms are discussed.
