Phase transitions in the fully frustrated triangularXYmodel

Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

“…It is the general belief that the transitions at T KT and at T I belong to the KT universality class [18] and to the Ising universality class, respectively, if the transitions occur at different temperatures. However, the critical exponents associated with the Z 2 symmetry breaking, which are found by Monte Carlo simulations, turn out to be different from those of the Ising universality [12,13,16]. They are rather close to those obtained in the XY -Ising model [5].…”

“…Monte Carlo simulation studies of the frustrated Coulomb gas system, which is supposed to be in the same universality class as the FFXY model, showed that the KT type transition temperature T KT and the Ising-like transition temperature T I are different with T KT < T I [11,12]. Two transitions were also found in the FFXY model on a square lattice [13] and on a triangular lattice [14][15][16] using Monte Carlo simulations. A careful analysis of the RG flow of the FFXY model also led to a conclusion of the double transition scenario [17].…”

“…On the other hand, more recent studies have reported the transitions to occur at two different temperatures [11][12][13][14][15][16][17]19,20,22]. Surprisingly, some of recent high-precision Monte Carlo simulation studies suggested that the Z 2 symmetry breaking transition does not belong to the Ising universality class in spite of the double transition [13,16,22]. They estimated that ν ≃ 0.8 for the correlation length exponent and α/ν ≃ 0.46 with the specific exponent α, which are incompatible with the Ising values of ν = 1 and α = 0.…”

“…Despite a lot of efforts [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], there is no consensus on the nature of the phase transitions and it is not clear whether the two transitions happen at two different temperatures or at a single one. Renormalization group (RG) studies on the FFXY model drew the conclusion that the transitions occur at the same temperature [3].…”

Nematic and Chiral Order for Planar Spins on a Triangular Lattice

“…This model contains the usual frustration in the exchange interaction due to the triangular lattice geometry, together with the possible nematic order induced by the J 2 term. The J 2 = 0 limit has been extensively studied, and it is believed to have two phase transitions at closely spaced critical temperatures [2,[13][14][15]. The Kosterlitz-Thouless (KT) transition temperature T KT signaling the loss of (algebraic) magnetic order and the melting temperature of the staggered chirality, T χ , are extremely close, (T χ − T KT )/T χ 0.02 at J 2 = 0, hampering the interpretation of the intermediate, T KT < T < T χ phase as the chiral phase in which the chirality is ordered but the magnetism remains disordered.…”