Frustrated triangular lattice

Geometrical frustration occurs when a set of degrees of freedom is incompatible with the space it occupies. A purely geometric example is the impossibility of close- packing pentagons in two dimensions. Another example is atomic magnetic moments with antiferromagnetic interactions. These moments lowers their interaction energy by pointing antiparallel to their neighbors. In case of two dimension, the triangular lattice is the simplest example. In triangular lattice the two spins can easily accommodate on two sides but the third spin is frustrated. If this third spin is up then two arrangement out of the three are compatible but one is incompatible. This leads to a huge degeneracy in the ground state with non-zero entropy. This frustration leads to breaking symmetry which leads to ferroelectricity.