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

Abstract

A transverse magnetic field $Γ$ is known to induce antiferromagnetic three-sublattice order of the Ising spins $σ^z$ 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 wavevector ${\bf Q}$: $\langle σ^z(\vec{R}) σ^z(0)\rangle \sim \cos({\mathbf Q}\cdot \vec{R}) /|\vec{R}|^{η(T)}$ with the temperature-dependent power-law exponent $η(T) \in (1/9,1/4)$. Here, we use a newly developed quantum cluster algorithm to study the {\em ferromagnetic} easy-axis susceptibility $χ_{u}(L)$ of an $L \times L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular $L$ dependence $χ_{u}(L)\sim L^{2- 9 η}$ when $η(T)$ is in the range $(1/9,2/9)$. This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility $χ_{u}(B)$ to a uniform field $B$ along the easy axis is singular at intermediate temperatures in the small $B$ limit, $χ_{u}(B) \sim |B|^{-\frac{4 - 18 η}{4-9η}}$ for $η(T) \in (1/9, 2/9)$, although there is no ferromagnetic long-range order in the low temperature state.