Damage spreading in two dimensional geometrically frustrated lattices: the triangular and kagome anistropic Heisenberg model

The technique of damage spreading is used to study the phase diagram of the easy axis anisotropic Heisenberg antiferromagnet on two geometrically frustrated lattices. The triangular and kagome systems are built up from triangular units that either share edges or corners respectively. The triangular lattice undergoes two sequential Kosterlitz-Thouless transitions while the kagome lattice undergoes a glassy transition. In both cases, the phase boundaries obtained using damage spreading are in good agreement with those obtained from equilibrium Monte Carlo simulations.Comment: 7 pages, 4 figure

Spin Stiffness of Stacked Triangular Antiferromagnets

We study the spin stiffness of stacked triangular antiferromagnets using both heat bath and broad histogram Monte Carlo methods. Our results are consistent with a continuous transition belonging to the chiral universality class first proposed by Kawamura.Comment: 5 pages, 7 figure

Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet

Ordering of the classical Heisenberg antiferromagnet on the triangular lattice is studied by means of a mean-field calculation, a scaling argument and a Monte Carlo simulation, with special attention to its vortex degree of freedom. The model exhibits a thermodynamic transition driven by the Z_2-vortex binding-unbinding, at which various thermodynamic quantities exhibit an essential singularity. The low-temperature state is a "spin-gel" state with a long but finite spin correlation length where the ergodicity is broken topologically. Implications to recent experiments on triangular-lattice Heisenberg antiferromagnets are discussed

Low-Temperature Excitations of Dilute Lattice Spin Glasses

A new approach to exploring low-temperature excitations in finite-dimensional lattice spin glasses is proposed. By focusing on bond-diluted lattices just above the percolation threshold, large system sizes $L$ can be obtained which lead to enhanced scaling regimes and more accurate exponents. Furthermore, this method in principle remains practical for any dimension, yielding exponents that so far have been elusive. This approach is demonstrated by determining the stiffness exponent for dimensions $d=3$, $d=6$ (the upper critical dimension), and $d=7$. Key is the application of an exact reduction algorithm, which eliminates a large fraction of spins, so that the reduced lattices never exceed $\sim10^3$ variables for sizes as large as L=30 in $d=3$, L=9 in $d=6$, or L=8 in $d=7$. Finite size scaling analysis gives $y_3=0.24(1)$ for $d=3$, significantly improving on previous work. The results for $d=6$ and $d=7$, $y_6=1.1(1)$ and $y_7=1.24(5)$, are entirely new and are compared with mean-field predictions made for d>=6.Comment: 7 pages, LaTex, 7 ps-figures included, added result for stiffness in d=7, as to appear in Europhysics Letters (see http://www.physics.emory.edu/faculty/boettcher/ for related information

Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice

The ordering of the classical Heisenberg antiferromagnet on the triangular lattice with the the bilinear-biquadratic interaction is studied by Monte Carlo simulations. It is shown that the model exhibits a topological phase transition at a finite-temperature driven by topologically stable vortices, while the spin correlation length remains finite even at and below the transition point. The relevant vortices could be of three different types, depending on the value of the biquadratic coupling. Implications to recent experiments on the triangular antiferromagnet NiGa$_2$S$_4$ is discussed

Monte Carlo Study of the Anisotropic Heisenberg Antiferromagnet on the Triangular Lattice

We report a Monte Carlo study of the classical antiferromagnetic Heisenberg model with easy axis anisotropy on the triangular lattice. Both the free energy cost for long wavelength spin waves as well as for the formation of free vortices are obtained from the spin stiffness and vorticity modulus respectively. Evidence for two distinct Kosterlitz-Thouless types of defect-mediated phase transitions at finite temperatures is presented.Comment: 8 pages, 10 figure

First-Order Transition to Incommensurate Phase with Broken Lattice Rotation Symmetry in Frustrated Heisenberg Model

We study a finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third-nearest-neighbor interaction $J_3$ using a Monte Carlo method. Apart from a trivial degeneracy corresponding to O(3) spin rotations,the ground state for $J_3 \neq 0$ has a threefold degeneracy corresponding to 120 degree lattice rotations. We find that this model exhibits a first-order phase transition with the breaking of the threefold symmetry when the interaction ratio is $J_3/J_1=-3$.Comment: 4pages,5figure

Evidence for the droplet/scaling picture of spin glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.Comment: 4 pages, 6 figure