Stiffness from disorder in triangular-lattice Ising thin films

Overlap of two topological phases in the antiferromagnetic Potts model

By controlling the vortex core energy, the three-state ferromagnetic Potts model can exhibit two types of topological paradigms, including the quasi-long-range ordered phase and the vortex lattice phase [Phys. Rev. Lett. 116, 097206 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.097206]. Here, using Monte Carlo simulations using an efficient worm algorithm, we show that by controlling the vortex core energy, the antiferromagnetic Potts model can also exhibit the two topological phases, and, more interestingly, the two topological phases can overlap with each other.

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.

Frustration and chiral orderings in correlated electron systems

The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson's proposal of a quantum spin liquid ground state for a two-dimensional lattice S  =  1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect.

Critical Exponents Can Be Different on the Two Sides of a Transition: A Generic Mechanism

We present models where γ(+) and γ(-), the exponents of the susceptibility in the high- and low-temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete anisotropies that are irrelevant in the renormalization-group sense. The Z(q)-invariant models are the simplest examples for two-component order parameters (N=2) and the model with icosahedral symmetry for N=3. We accurately compute γ(+)-γ(-) as well as the ratio ν/ν' of the exponents of the two correlation lengths present for T<T(c).

Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment

In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multispin U(1) order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type, and at lower temperatures we find long-range Z(6) order.