Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

A transverse magnetic field Gamma is known to induce antiferromagnetic three-sublattice order of the Ising spins sigma(z) in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector Q: <sigma(z)((R) over right arrow) sigma(z)(0)> similar to cos(Q.(R) over right arrow)/vertical bar(R) over right arrow vertical bar(eta(T)) with the temperature-dependent power-law exponent eta(T) is an element of (1/9,1/4). Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility chi(u) (L) of an L x L sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular L dependence chi(u) (L) similar to L2-9 eta when eta(T) is in the range (1/9,2/9). This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility chi(u) (B) to a uniform field B along the easy axis is singular at intermediate temperatures in the small B limit, chi(u) (B) similar to vertical bar B vertical bar(-4-18 eta/4-9 eta) for eta(T) is an element of (1/9,2/9), although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility chi(Q)) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (J(2)) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.