We consider the dynamics of interpersonal relations which leads to balanced states in a fully connected network. Here this approach is applied to directed networks with asymmetric relations, and it is generalized to include self-evaluation of actors, according to the ‘looking-glass self’ theory. A new index of self-acceptance is proposed: the relation of an actor to him/herself is positive, if the majority of his/her positive relations to others are reciprocated. Sets of stable configurations of relations are obtained under the dynamics, where the self-evaluation of some actors is negative. Within each set all configurations have the same structure.

We investigate magnetic properties of a two-dimensional periodic structure with Ising spins and antiferromagnetic nearest-neighbor interaction. The structure is topologically equivalent to the Archimedean $(3,{12}^2)$ lattice. The ground state energy is degenerate. In some ground states, the spin structure is translationally invariant, with the same configuration in each unit cell. Numerical results are reported on specific heat and static magnetic susceptibility against temperature. Both quantities show maxima at temperature $T>0$. They reveal some sensitivity on the initial state in temperatures where the Edwards–Anderson order parameter is positive. For zero temperature and low frequency of the applied field, the magnetic losses are negligible. However, the magnetization curve displays some erratic behavior due to the metastable states.