Low-temperature phase of a stacked triangular Ising antiferromagnet

Ordering phenomena in a heterostructure of frustrated and unfrustrated triangular-lattice Ising layers

We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling J_{A} and the ferromagnetic (FM) one J_{B} for the respective layers, which are coupled by the interlayer interaction J_{AB} by using Monte Carlo simulations. When J_{A} and J_{B} are of the same order, the unfrustrated FM plane orders first at a high temperature T_{c1}∼J_{B}. The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequently induces a ferrimagnetic order in this plane at low temperatures below T_{c2}. When short-range order is developed in the AF plane while the influence of the FM plane is still small, there appears a preemptive Berezinskii-Kosterlitz-Thouless-type pseudocritical crossover regime just above the ferrimagnetic phase transition point, where the short-distance behavior up to a rather large length scale exponentially diverging in ∝J_{A}/T is controlled by a line of Gaussian fixed points at T=0. In the crossover region, a continuous variation in the effective critical exponent 4/9≲η^{eff}≲1/2 is observed. The phase diagram by changing the ratio J_{A}/J_{B} is also investigated.

Stiffness from disorder in triangular-lattice Ising thin films

We study the triangular lattice Ising model with a finite number of vertically stacked layers and demonstrate a low temperature reentrance of two Berezinskii-Kosterlitz-Thouless transitions, which results in an extended disordered regime down to T=0. Numerical results are complemented with the derivation of an effective low-temperature dimer theory. Contrary to order by disorder, we present a new scenario for fluctuation-induced ordering in frustrated spin systems. While short-range spin-spin correlations are enhanced by fluctuations, quasi-long-range ordering is precluded at low enough temperatures by proliferation of topological defects.

Effects of geometrical frustration on the spin-glass transition

Randomness and frustration are important for the spin-glass transitions. Ising antiferromagnet on a stacked triangular lattice is a highly frustrated system. Phase diagram is obtained within a cluster approximation for the system with randomness in the interaction between Ising spins. To see the frustration effects, the phase diagram of the antiferromagnet is compared with the corresponding one of the ferromagnet. Spin-glass phase of the antiferromagnet appears much more easily by the randomness than that of the ferromagnet.

Triangular Ising antiferromagnets with quenched nonmagnetic impurities

In a random spin system, the cooperation of randomness and frustration will lead to a spin-glass phase. However, in geometrically frustrated spin systems, quenched nonmagnetic impurities lift frustration locally. This makes randomness and frustration in these systems as competitors rather than cooperators. By mapping the dilute triangular Ising antiferromagnetic system to elastic array of noncrossing strings, we find that the nonmagnetic impurities in the spin system play roles of pinning centers in the string system. Calculation shows that in the ground state of this system, the spin-glass correlation is power-law decayed, quite different from the standard behavior of spin glass in which spin-glass correlation between two spins at infinite distance tends to a finite value. This indicates that triangular Ising antiferromagnets with quenched nonmagnetic impurities cannot be a spin glass. Instead, in the ground states, they present properties of vortex glass.

String picture for a model of frustrated quantum magnets and dimers

We study the effect of quantum dynamics on geometrically frustrated magnets for a transverse field Ising model at finite temperatures. We develop a microscopic derivation of the Landau-Ginzburg-Wilson action for this model and show that it can be interpreted as the free energy of a 3D elastic lattice of noncrossing strings. As a first application, we quantitatively predict the phase diagram and correlations, confirming excellently a key prediction of recent simulations about the existence of unusual phase transitions and an ordered phase. We discuss the implications of our string picture for the understanding of the effect of quenched disorder in such quantum frustrated systems.