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The spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied by mean-field method. The thermal variations of order parameters and phase diagrams are investigated in detail. The stable,…
I review recent developments in determining the QCD phase diagram by means of lattice simulations. Since the invention of methods to side-step the sign problem a few years ago, a number of additional variants have been proposed, and…
The control of discrete quantum states in solids and their use for quantum information processing is complicated by the lack of a detailed understanding of the mechanisms responsible for qubit decoherences. For spin qubits in semiconductor…
We analyze the zero temperature phase diagrams of the spin S quantum antiferromagnet on square and triangular lattices with competing nearest and next-nearest exchange interactions as well as biquadratic couplings. We approach the problem…
A special family of solvable five-vertex model is introduced on a square lattice. In addition to the usual nearest neighbor interactions, the vertices defining the model also interact alongone of the diagonals of the lattice. Such family of…
The Ising spin glass model in a transverse field has a zero temperature phase transition driven solely by quantum fluctuations. This quantum phase transition occuring at a critical transverse field strength has attracted much attention…
We investigate a spinless Fermi gas trapped in a honeycomb optical lattice with attractive nearest-neighbor interactions. At zero temperature, mean-field theory predicts three quantum phase transitions, two being topological. At low…
The melting transitions of a colloidal lattice confined to a two-dimensional ($2D$) periodic substrate of square symmetry are studied using Monte Carlo simulations. When the strengths of interparticle and particle-substrate interactions are…
Physical phenomena driven by topological properties, such as the quantum Hall effect, have the appealing feature to be robust with respect to external perturbations. Lately, a new class of materials has emerged manifesting their topological…
Dynamical effects under geometrical frustration are considered in a model for artificial spin ice on a square lattice in two dimensions. Each island of the spin ice has a three-component Heisenberg-like dipole moment subject to shape…
Using a combined analysis from Poisson-Dirichlet and symmetry-breaking calculations as well as quantum Monte Carlo simulations, we examine the ordered phase and the thermal phase transition of the three-dimensional spin-1 quantum magnet on…
The dynamic phase transitions have been studied, within a mean-field approach, in the kinetic spin-1 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time varying (sinusoidal) magnetic…
Collective dynamics in lithographically-defined artificial spin ices offer profound insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution are often…
We present a numerical study of the random Blume-Capel model in three dimension. The phase diagram is characterized by spin-glass/paramagnet phase transitions both of first and second order in the thermodynamic sense. Numerical simulations…
We consider both equilibrium and kinetic aspects of the phase separation (``thermal faceting") of thermodynamically unstable crystal surfaces into a hill--valley structure. The model we study is an Ising lattice gas for a simple cubic…
We study a three-dimensional plaquette spin model whose low temperature dynamics is glassy, due to localised defects and effective kinetic constraints. While the thermodynamics of this system is smooth at all temperatures, we show that…
Chirality of materials in nature appears when there are asymmetries in their lattice structures or interactions in a certain environment. Recent development of quantum simulation technology has enabled the manipulation of qubits.…
We study the phase diagram of spin-one polar condensates in a two dimensional optical lattice with magnetic anisotropy. We show that the topological binding of vorticity to nematic disclinations allows for a rich variety of phase…
Dynamics of vortices in strongly type-II superconductors with strong disorder is investigated within the frustrated three-dimensional XY model. For two typical models in [Phys. Rev. Lett. {\bf 91}, 077002 (2003)] and [Phys. Rev. B {\bf 68},…
Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8…