Phase transition of the three-dimensional chiral Ginzburg-Landau model -- search for the chiral phase

Nature of the phase transition of regularly frustrated vector spin systems in three dimensions is investigated based on a Ginzburg-Landau-type effective Hamiltonian. On the basis of the variational analysis of this model, Onoda et al recently suggested the possible occurrence of a chiral phase, where the vector chirality exhibits a long-range order without the long-range order of the spin [Phys. Rev. Lett. 99, 027206 (2007)]. In the present paper, we elaborate their analysis by considering the possibility of a first-order transition which was not taken into account in their analysis. We find that the first-order transition indeed occurs within the variational approximation, which significantly reduces the stability range of the chiral phase, while the chiral phase still persists in a restricted parameter range. Then, we perform an extensive Monte Carlo simulation focusing on such a parameter range. Contrary to the variational result, however, we do not find any evidence of the chiral phase. The range of the chiral phase, if any, is estimated to be less than 0.1% in the temperature width.Comment: 19 pages, 17 figure

Study of Chirality in the Two-Dimensional XY Spin Glass

We study the chirality in the Villain form of the XY spin glass in two--dimensions by Monte Carlo simulations. We calculate the chiral-glass correlation length exponent $\nu_{\scriptscriptstyle CG}$ and find that $\nu_{\scriptscriptstyle CG} = 1.8 \pm 0.3$ in reasonable agreement with earlier studies. This indicates that the chiral and phase variables are decoupled on long length scales and diverge as $T \to 0$ with {\em different} exponents, since the spin-glass correlation length exponent was found, in earlier studies, to be about 1.0.Comment: 4 pages. Latex file and 4 embedded postscript files are included in a self-unpacking compressed tar file. A postscript version is available at ftp://chopin.ucsc.edu/pub/xysg.p

Finite Temperature Dynamics of the Spin 1/2 Bond Alternating Heisenberg Antiferromagnetic Chain

We present results for the dynamic structure factor of the S=1/2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\lambda \approx 0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the S=1 bound state which remains well defined up to temperatures of the order of J. The variation with temperature and wavevector of the integrated intensity for one and two magnon scattering and of the central peak are discussed.Comment: 8 pages, 8 figure

Global fluctuations and Gumbel statistics

We explain how the statistics of global observables in correlated systems can be related to extreme value problems and to Gumbel statistics. This relationship then naturally leads to the emergence of the generalized Gumbel distribution G_a(x), with a real index a, in the study of global fluctuations. To illustrate these findings, we introduce an exactly solvable nonequilibrium model describing an energy flux on a lattice, with local dissipation, in which the fluctuations of the global energy are precisely described by the generalized Gumbel distribution.Comment: 4 pages, 3 figures; final version with minor change

Ground states and thermal states of the random field Ising model

The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random and external field strength. Thermal states and thermodynamic properties are obtained for all temperatures using the the Wang-Landau algorithm. The specific heat and susceptibility typically display sharp peaks in the critical region for large systems and strong disorder. These sharp peaks result from large domains flipping. For a given realization of disorder, ground states and thermal states near the critical line are found to be strongly correlated--a concrete manifestation of the zero temperature fixed point scenario.Comment: 5 pages, 5 figures; new material added in this versio

Numerical study of the random field Ising model at zero and positive temperature

In this paper the three dimensional random field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the bond energy. The heat capacity exponent $\alpha$ is found to be near zero. The ground states are determined for a range of external field and disorder strength near the zero temperature critical point and the scaling of ground state tilings of the field-disorder plane is discussed. At positive temperature the specific heat and the susceptibility are obtained using the Wang-Landau algorithm. It is found that sharp peaks are present in these physical quantities for some realizations of systems sized $16^3$ and larger. These sharp peaks result from flipping large domains and correspond to large discontinuities in ground state bond energies. Finally, zero temperature and positive temperature spin configurations near the critical line are found to be highly correlated suggesting a strong version of the zero temperature fixed point hypothesis.Comment: 11 pages, 14 figure

Effects of semiclassical spiral fluctuations on hole dynamics

We investigate the dynamics of a single hole coupled to the spiral fluctuations related to the magnetic ground states of the antiferromagnetic J_1-J_2-J_3 Heisenberg model on a square lattice. Using exact diagonalization on finite size clusters and the self consistent Born approximation in the thermodynamic limit we find, as a general feature, a strong reduction of the quasiparticle weight along the spiral phases of the magnetic phase diagram. For an important region of the Brillouin Zone the hole spectral functions are completely incoherent, whereas at low energies the spectral weight is redistributed on several irregular peaks. We find a characteristic value of the spiral pitch, Q=(0.7,0.7)\pi, for which the available phase space for hole scattering is maximum. We argue that this behavior is due to the non trivial interference of the magnon assisted and the free hopping mechanism for hole motion, characteristic of a hole coupled to semiclassical spiral fluctuations.Comment: 6 pages, 5 figure

Effect of weak disorder in the Fully Frustrated XY model

The critical behaviour of the Fully Frustrated XY model in presence of weak positional disorder is studied in a square lattice by Monte Carlo methods. The critical exponent associated to the divergence of the chiral correlation length is found to be equal to 1.7 already at very small values of disorder. Furthermore the helicity modulus jump is found larger than the universal value expected in the XY model.Comment: 8 pages, 4 figures (revtex

Emergent gauge dynamics of highly frustrated magnets

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern-Simons electrodynamics expected of a $Z_2$ spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step towards a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and towards a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and some additional improvements. 21 pages, 5 figure

Conserved Growth on Vicinal Surfaces

A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo, and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A one--loop dynamical renormalization group calculation yields the values of the dynamical exponent and the roughness exponent which are shown to be the same as in the isotropic case. The results presented here should apply in particular to growth under conditions which are typical for molecular beam epitaxy.Comment: 10 pages, uses revte