Geometric criticality between plaquette phases in integer-spin kagome XXZ antiferromagnets

The phase diagram of the uniaxially anisotropic $s=1$ antiferromagnet on the kagom\'e lattice includes a critical line exactly described by the classical three-color model. This line is distinct from the standard geometric classical criticality that appears in the classical limit ($s \to \infty$) of the 2D XY model; the $s=1$ geometric T=0 critical line separates two unconventional plaquette-ordered phases that survive to nonzero temperature. The experimentally important correlations at finite temperature and the nature of the transitions into these ordered phases are obtained using the mapping to the three-color model and a combination of perturbation theory and a variational ansatz for the ordered phases. The ordered phases show sixfold symmetry breaking and are similar to phases proposed for the honeycomb lattice dimer model and $s=1/2$ $XXZ$ model. The same mapping and phase transition can be realized also for integer spins $s \geq 2$ but then require strong on-site anisotropy in the Hamiltonian.Comment: 5 pages, 2 figure

Zero Temperature Dynamics of the Weakly Disordered Ising Model

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P(t)\sim L(t)^{-\theta'}$, where $\theta' = 0.420\pm 0.009$. The value of $\theta'$ is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P(t)\sim (\ln t)^{-\theta_d}$, where $\theta_d = 0.63\pm 0.01$.Comment: references updated, very minor amendment to abstract and the labelling of figures. To be published in Phys Rev E (Rapid Communications), 1 March 199

Interfering directed paths and the sign phase transition

We revisit the question of the "sign phase transition" for interfering directed paths with real amplitudes in a random medium. The sign of the total amplitude of the paths to a given point may be viewed as an Ising order parameter, so we suggest that a coarse-grained theory for system is a dynamic Ising model coupled to a Kardar-Parisi-Zhang (KPZ) model. It appears that when the KPZ model is in its strong-coupling ("pinned") phase, the Ising model does not have a stable ferromagnetic phase, so there is no sign phase transition. We investigate this numerically for the case of {\ss}1+1 dimensions, demonstrating the instability of the Ising ordered phase there.Comment: 4 pages, 4 figure

The short-time Dynamics of the Critical Potts Model

The universal behaviour of the short-time dynamics of the three state Potts model in two dimensions at criticality is investigated with Monte Carlo methods. The initial increase of the order is observed. The new dynamic exponent $\theta$ as well as exponent $z$ and $\beta/\nu$ are determined. The measurements are carried out in the very beginning of the time evolution. The spatial correlation length is found to be very short compared with the lattice size.Comment: 6 pages, 3 figure

Loop models and their critical points

Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm-Loewner evolution. I present new loop models which have critical points described by conformal field theories. Examples include both fully-packed and dilute loop models with critical points described by the superconformal minimal models and the SU(2)_2 WZW models. The dilute loop models are generalized to include SU(2)_k models as well.Comment: 20 pages, 15 figure

Universality and Crossover of Directed Polymers and Growing Surfaces

We study KPZ surfaces on Euclidean lattices and directed polymers on hierarchical lattices subject to different distributions of disorder, showing that universality holds, at odds with recent results on Euclidean lattices. Moreover, we find the presence of a slow (power-law) crossover toward the universal values of the exponents and verify that the exponent governing such crossover is universal too. In the limit of a 1+epsilon dimensional system we obtain both numerically and analytically that the crossover exponent is 1/2.Comment: LateX file + 5 .eps figures; to appear on Phys. Rev. Let

Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice

We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system remains short-range ordered independent of the sign and the strength of the interlayer coupling

Determination of the Critical Point and Exponents from short-time Dynamics

The dynamic process for the two dimensional three state Potts model in the critical domain is simulated by the Monte Carlo method. It is shown that the critical point can rigorously be located from the universal short-time behaviour. This makes it possible to investigate critical dynamics independently of the equilibrium state. From the power law behaviour of the magnetization the exponents $\beta / (\nu z)$ and $1/ (\nu z)$ are determined.Comment: 6 pages, 4 figure

End to end distance on contour loops of random gaussian surfaces

A self consistent field theory that describes a part of a contour loop of a random Gaussian surface as a trajectory interacting with itself is constructed. The exponent \nu characterizing the end to end distance is obtained by a Flory argument. The result is compared with different previuos derivations and is found to agree with that of Kondev and Henley over most of the range of the roughening exponent of the random surface.Comment: 7 page

On the theory of diamagnetism in granular superconductors

We study a highly disordered network of superconducting granules linked by weak Josephson junctions in magnetic field and develop a mean field theory for this problem. The diamagnetic response to a slow {\it variations} of magnetic field is found to be analogous to the response of a type-II superconductor with extremely strong pinning. We calculate an effective penetration depth $\lambda_g$ and critical current $j_c$ and find that both $\lambda_g^{-1}$ and $j_c$ are non-zero but are strongly suppressed by frustration.Comment: REVTEX, 12 pages, two Postscript figure