  Structural balance in social complex networks has been modeled with two types
of triplet interactions. First, the interaction that only considers dynamic
role for links or relationships (Heider balance), and second, the interaction
that considers both individual opinions (nodes) and relationships in network
dynamics (coevolutionary balance). The question is, as the temperature varies,
which is a measure of social disorder, how structural balance can be created or
destroyed by each of these triplet interactions? We use statistical mechanics
methods and observe through analytical calculation and numerical simulation
that unlike the Heider balance triplet interaction which has a discrete phase
transition, the coevolutionary balance has a continuous phase transition. The
critical temperature of the presented model change with the root square of
network size which is a linear dependence in thermal Heider balance.
