We provide an effective description of a triangular-lattice model with a three-spin interaction. On the basis of a symmetry consideration, we argue that a vector dual sine-Gordon field theory is relevant, and provides us a framework to analyze long-distance behaviors. In particular, we can characterize a criticality of an intermediate phase between the low- and high-temperature phases. Also, in comparison with a model on the Union Jack lattice, we explain that the sublattice symmetry of the triangular lattice plays a crucial role to exhibit a novel phase transition. Theoretical predictions obtained are then confirmed by numerical calculations.
We discuss an effective field theory of a triangular-lattice three-spin interaction model defined by the
Zp variables. Based on the symmetry properties and the ideal-state graph concept, we show that the vector dual sine-Gordon model describes the long-distance properties for
p≥5; we then compare its predictions with the previous argument. To provide the evidences, we numerically analyze the eigenvalue structure of the transfer matrix for
p=6, and we check the criticality with the central charge
c=2 of the intermediate phase and the quantization condition of the vector charges.
We study a Berezinskii-Kosterlitz-Thouless-like phase transition in a triangular-lattice three-spin interaction model. The vector sine-Gordon field theory describes defects involved, and enables us to perform the renormalization-group analysis of the transition. Based on it, we discuss properties of the spin-spin correlation function, and also analyze the helicity modulus for the present model. To provide the data to support our analysis, we perform the Monte-Carlo simulations to calculate them. Further, we exhibit snapshots of some typical defect conflgurations, which are helpful to illustrate the defect-mediated phase transition.
We investigate infinite-order phase transitions like the Berezinskii-Kosterlitz-Thouless transition observed in a triangular-lattice three-spin interaction model. Based on a field theoretical description and the operator-production-expansion technique, we perform the renormalization-group analysis, and then clarify properties of marginal operators near the phase transition points. The results are utilized to establish criteria to determine the transition points and some universal relations among excitation levels to characterize the transitions. We verify these predictions via the numerical analysis on eigenvalue structures of the transfer matrix. Also, we discuss an enhancement of symmetry at the end points of a critical intermediate phase in connection with a transition observed in the ground state of the bilinear-biquadratic spin-1 chain.
A transverse magnetic field $\mathrm{\ensuremath{\Gamma}}$ is known to induce antiferromagnetic three-sublattice order of the Ising spins ${\ensuremath{\sigma}}^{z}$ 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: $\ensuremath{\langle}{\ensuremath{\sigma}}^{z}(\stackrel{P\vec}{R}){\ensuremath{\sigma}}^{z}(0)\ensuremath{\rangle}\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{R})/{|\stackrel{P\vec}{R}|}^{\ensuremath{\eta}(T)}$ with the temperature-dependent power-law exponent $\ensuremath{\eta}(T)\ensuremath{\in}(1/9,1/4)$. Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility ${\ensuremath{\chi}}_{u}(L)$ of an $L\ifmmode\times\else\texttimes\fi{}L$ sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular
L dependence ${\ensuremath{\chi}}_{u}(L)\ensuremath{\sim}{L}^{2\ensuremath{-}9\ensuremath{\eta}}$ when $\ensuremath{\eta}(T)$ is in the range
(1/9,2/9). This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility ${\ensuremath{\chi}}_{u}(B)$ to a uniform field
B along the easy axis is singular at intermediate temperatures in the small
B limit, ${\ensuremath{\chi}}_{u}(B)\ensuremath{\sim}{|B|}^{\ensuremath{-}\frac{4\ensuremath{-}18\ensuremath{\eta}}{4\ensuremath{-}9\ensuremath{\eta}}}$ for $\ensuremath{\eta}(T)\ensuremath{\in}(1/9,2/9)$, 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 ${\ensuremath{\chi}}_{\mathbf{Q}}$) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (
J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.
We propose a non-disordered antiferromagnetic Heisenberg spin model on a triangular lattice, which exhibits a critical state and a glassy state at low temperatures. The system has three phases, the paramagnetic, the intermediate critical, and the glassy phase. The intermediate phase is characterized by a quasi-long-range order, whereas only short-range order exists in the glassy phase. Using Monte Carlo simulation, the phase transitions and properties of the two phases at low temperatures are examined. Our spin model shows that the variable-length spin and the competition between bilinear and biquadratic interactions are essential for forming the critical and glassy phases.
By Monte Carlo simulations we study critical properties of the mixed spin-1/2 and spin-1 Ising model on a triangular lattice, considering two different ways of the spin-value distributions on the three sublattices: (1/2,1/2,1) and (1/2,1,1). In the former case, we find standard Ising universality class phase transitions between paramagnetic and magnetic phases but no phase transitions between two distinct magnetic phases (±1/2,±1/2,±1) and (±1/2,±1/2,0) at any finite temperature, except for some interesting non-critical anomalies displayed by response functions. On the other hand, the latter case turns out to be a rare (or perhaps the only) example of a two-dimensional mixed spin-1/2 and spin-1 Ising model on a standard lattice that displays tricritical behavior.