二维完全阻挫XY模型的动力学指数

采用大规模动力学蒙特卡罗模拟方法,对二维完全阻挫XY模型的Kosterlitz-Thouless(KT)型相变展开数值研究.系统从有序初始态出发演化到高于KT相变的温度,以普适的动力学标度形式为基础,通过测量磁化和Binder累积量,得出动力学关联时间和平衡态空间关联长度,确定出更精确的动力学指数z.特别是建议并证实了一种在KT相变温度以上(T>TKT),独立判断动力学指数z的方法.模拟结果表明,动力学指数z≈2,这与在相变温度以下(T     

Short-time dynamic behavior of the two-dimensional square lattice fully frustrated XY model

The short-time dynamic behavior of the two-dimensional fully frustrated XY model on a square lattice with ferromagnetic and antiferromagnetic couplings arranged in a zigzag pattern near the critical temperature is investigated. The Ising-like phase transition temperature T_c and all the static and dynamic critical exponents 2β/ν, ν and z are determined for two definitions of order parameter: the staggered chiral magnetization M_χ and the staggered magnetization M_st. We find that T_c, 2β/ν and z are almost independent of the definition of order parameter: T_c=0.4544(2), 2β/ν=0.265(4) and z=2.24(3) for M_χ while they are 0.4546(2), 0.274(4) and 2.25(3) for M_st, respectively. But ν depends on the definition of order parameter, ν=0.813(13) for M_χ while it is 0.862(16) for M_st.     

The phase transition in the fully frustrated XY model as a percolation problem

The fully frustrated planar rotator and fully frustrated XY models in two dimensions have two phase transitions: one of the Berezinskii–Kosterlitz–Thouless type and other in the Ising universality class. We use Monte Carlo simulation to study both models. We fix our attention in the Ising-like transition, which we show can be understood as a percolation transition. We obtain the critical temperature as well as the critical exponents of the mean cluster size, γ, and Fisher's exponent τ. The critical temperature agree very well with other calculations. We found that the critical exponents are smaller than in the pure two-dimensional percolation case. We interpret this as due to the long-range interaction between vortex and antivortex.     

Fluctuations and vortex-pattern ordering in the fully frustrated XY model on a honeycomb lattice

The accidental degeneracy of various ground states of a fully frustrated XY model with a honeycomb lattice is shown to survive even when the free energy of the harmonic fluctuations is taken into account. The reason for that consists in the existence of a hidden gauge symmetry between the Hamiltonians describing the harmonic fluctuations in all these ground states. A particular vortex pattern is selected only when anharmonic fluctuations are taken into account. However, the observation of vortex ordering requires relatively large system size L>Lc > or approximately equal to 10(5).     

Site dilution in the fully frustrated triangular lattice in two dimensions

The Transfermatrix-Method [1, 2] has been adapted to evaluate also the free energy of triangular 2–d-Ising lattices. The present work considers a model with nearest-neighbour antiferromagnetic couplings and a fraction 1–x of spins removed at random sites leading to some frustration effects. It is not yet clear if such a system shows spinglass behaviour [3, 4]. The correlation function s ₀ s _R ² (correlation between two spins with distanceR), which is related to the Edwards-Anderson-Orderparameter, shows such a fast breakdown with distanceR that there is a clear evidence against a phase transition at finiteT. In contrast to other models [1, 2, 5] we still expect an exponential decay of {s ₀ s _R ²} _av with distanceR atT=0.     

Uniformly frustrated XY model without a vortex-pattern ordering

The uniformly frustrated XY model with f=1/3 on a dice lattice is shown to possess an accidental degeneracy of its ground states so well developed that the difference between the free energies of fluctuations does not lead to the stabilization of a particular vortex pattern down to zero temperature. Nonetheless, at low temperatures the system is characterized by a finite helicity modulus whose vanishing (at a finite temperature) is related to the dissociation of half-vortex pairs.     

Kaleidoscope of exotic quantum phases in a frustrated XY model

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought for Bose metal with a clearly identifiable Bose surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions.     

Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of ³He-⁴He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.     

Non-equilibrium phase transition of the fully frustrated square lattice Coulomb gas model

The non-equilibrium phase transitions of the fullyfrustrated (f = 1/2) square lattice Coulomb gas (CG) modeldriven by external electrical fields are studied in the frameworkof the short-time dynamic scaling approach. The criticaltemperature T_c, the static and dynamic critical exponents2β/ν, ν, and z are obtained for several smalldriving fields. The results show that T_c decreases with theincrease of electric field, and 2β/ν and z arestrongly dependent on the external electric field. Interestingly,contrary to the equilibrium case, in the presence of smallelectric field, the calculated exponent ν is close to that inpure 2D Ising model, which provides numerical evidence thatexternal electric field may change the universality class of thef = 1/2 CG system.     

A frustrated planar XY model for niobia–zirconia ceramic alloys

A model is proposed for the structurally complex ceramic superlattice alloys of niobia and zirconia of stoichiometry Nb₂Zr_x−2O_2x+1 (7.1< x<10.3), in which transformation between the locally tetragonal and hexagonal segments of the characteristic oxygen ion nets can be interpreted as arrays of periodically-spaced rotations of anions. These rotatable regions are the elastic analogy of magnetic XY spins. Evidence is discussed for geometrical frustration in the nets, which, in combination with their XY character, can explain many of the apparent anomalies associated with the niobia–zirconia alloys.