We investigate a first-order phase transition from a non-magnetic phas
e to a non-frustrated phase of a two-dimensional triangular lattice wi
th antiferromagnetic bonds. A cellular automaton is defined, which cho
oses a magnetic state of subsequent lattice sites, where an interphase
boundary arrives, as to minimise the local energy. The ground state m
agnetic state is found to be unstable with respect to the point defect
s of magnetic structure.