Nature of phase transitions in the striped phase of a triangular-lattice Ising antiferromagnet

Different scenarios of the fluctuation-induced disordering of the striped phase which is formed at low temperatures in the triangular-lattice Ising model with the antiferromagnetic interaction of nearest and further neighbors are analyzed and compared. The dominant mechanism of the disordering is related to the formation of a network of domain walls, which is characterized by an extensive number of zero modes and has to appear via the first-order phase transition. In principle, this first-order transition can be preceded by a continuous one, related to the spontaneous formation of double domain walls and a partial restoration of the broken symmetry, but the realization of such a scenario requires the fulfillment of rather special relations between the coupling constants.

Figure 1

The structure of the ground state for $J_{1,2}>0$.

Figure 2

The classification of neighbors on triangular lattice.

Figure 3

Low energy domain walls: (a) a straight one; (b) with a kink.

Figure 4

Double domain walls: (a) straight; (b) with two corners.

Figure 5

Closed loops formed by (a) single domain walls, (b) double domain walls.

Figure 6

Three low-energy domain walls with different orientations can merge or intersect with each other.

Figure 7

A possible structure of a domain-wall network.