3D loop models and the CP^{n-1} sigma model

Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to $CP^{n-1}$ sigma models, where $n$ is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for $n=1,2,3$, and first order transitions for $n\geq 5$. The results are relevant to line defects in random media, as well as to Anderson localization and $(2+1)$-dimensional quantum magnets.Comment: Published versio

Magnetic field induced finite size effect in type-II superconductors

We explore the occurrence of a magnetic field induced finite size effect on the specific heat and correlation lengths of anisotropic type-II superconductors near the zero field transition temperature Tc. Since near the zero field transition thermal fluctuations are expected to dominate and with increasing field strength these fluctuations become one dimensional, whereupon the effect of fluctuations increases, it appears unavoidable to account for thermal fluctuations. Invoking the scaling theory of critical phenomena it is shown that the specific heat data of nearly optimally doped YBa2Cu3O7-x are inconsistent with the traditional mean-field and lowest Landau level predictions of a continuous superconductor to normal state transition along an upper critical field Hc2(T). On the contrary, we observe agreement with a magnetic field induced finite size effect, whereupon even the correlation length longitudinal to the applied field H cannot grow beyond the limiting magnetic length L(H). It arises because with increasing magnetic field the density of vortex lines becomes greater, but this cannot continue indefinitely. L(H) is then roughly set on the proximity of vortex lines by the overlapping of their cores. Thus, the shift and the rounding of the specific heat peak in an applied field is traced back to a magnetic field induced finite size effect in the correlation length longitudinal to the applied field.Comment: 8 pages, 4 figure

Kondo lattice on the edge of a two-dimensional topological insulator

We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling which was missed by previous poor man's scaling treatments. The combination of an exact solution at the so-called decoupling point and a renormalization group analysis \`a la Anderson-Yuval-Hamann allows us to access the regime of strong electron-electron interactions on the edge and strong Kondo coupling. We apply similar methods to the problem of a regular one-dimensional array of quantum impurities interacting with the edge liquid. When the edge electrons are at half-filling with respect to the impurity lattice, the system remains gapless unless the Luttinger parameter of the edge is less than 1/2, in which case two-particle backscattering effects drive the system to a gapped phase with long-range Ising antiferromagnetic order. This is in marked contrast with the gapped disordered ground state of the ordinary half-filled one-dimensional Kondo lattice.Comment: 18 pages, 3 figures; fixed typos, updated reference

Edge Logarithmic Corrections probed by Impurity NMR

Semi-infinite quantum spin chains display spin autocorrelations near the boundary with power-law exponents that are given by boundary conformal field theories. We show that NMR measurements on spinless impurities that break a quantum spin chain lead to a spin-lattice relaxation rate 1/T_1^edge that has a temperature dependence which is a direct probe of the anomalous boundary exponents. For the antiferromagnetic S=1/2 spin chain, we show that 1/T_1^edge behaves as T (log T)^2 instead of (log T)^1/2 for a bulk measurement. We show that, in the case of a one-dimensional conductor described by a Luttinger liquid, a similar measurement leads to a relaxation rate 1/T_1^{edge} behaving as T, independent of the anomalous exponent K_rho.Comment: 4 pages, 1 encapsulated figure, corrected typo

Bifurcation at the c=3/2 Takhtajan-Babujian point to the c=1 critical lines

We study the S=1 quantum spin chains with bilinear, biquadratic, plus bond alternation in the vicinity of the S=1 Takhtajan-Babujian model. Transition line between the Haldane and the dimer phases are determined numerically. To see the crossover behavior from c=3/2 (k=2 SU(2) WZW model) at the Takhtajan-Babujian point to c=1 (k=1 SU(2) WZW model), we calculate the conformal anomaly c and scaling dimensions of the primary fields on the transition line.Comment: 10 pages, 8 figure

Matter Wave Turbulence: Beyond Kinetic Scaling

Turbulent scaling phenomena are studied in an ultracold Bose gas away from thermal equilibrium. Fixed points of the dynamical evolution are characterized in terms of universal scaling exponents of correlation functions. The scaling behavior is determined analytically in the framework of quantum field theory, using a nonperturbative approximation of the two-particle irreducible effective action. While perturbative Kolmogorov scaling is recovered at higher energies, scaling solutions with anomalously large exponents arise in the infrared regime of the turbulence spectrum. The extraordinary enhancement in the momentum dependence of long-range correlations could be experimentally accessible in dilute ultracold atomic gases. Such experiments have the potential to provide insight into dynamical phenomena directly relevant also in other present-day focus areas like heavy-ion collisions and early-universe cosmology.Comment: 18 pages, 2 figure

Percolation in real Wildfires

This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite imagery are analysed. Results indicate that the burned clusters behave similarly to percolation clusters on boundaries and look more dense in their core. We show that Dynamical Percolation reproduces this behaviour and can help to describe the fire evolution. By mapping fire dynamics onto the percolation models the strategies for fire control might be improved.Comment: 8 pages, 3 figures, epl sytle (epl.cls included

Exact Critical Properties of the Multi-Component Interacting Fermion Model with Boundaries

Exact critical properties of the one-dimensional SU($N$) interacting fermion model with open boundaries are studied by using the Bethe ansatz method. We derive the surface critical exponents of various correlation functions using boundary conformal field theory. They are classified into two types, i.e. the exponents for the chiral SU($N$) Tomonaga-Luttinger liquid and those related to the orthogonality catastrophe. We discuss a possible application of the results to the photoemission (absorption) in the edge state of the fractional quantum Hall effect.Comment: 17 pages, RevTe

Phase diagram of S=1 XXZ chain with next-nearest neighbor interaction

The one dimensional S=1 XXZ model with next-nearest-neighbor interaction $\alpha$ and Ising-type anisotropy $\Delta$ is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the N\'{e}el phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear $\sigma$ model and analyze the phase diagram in the $\alpha$ $\ll$ -1 and $\Delta$ $\sim$ 1 region by using the renormalization group method.Comment: 18 pages, 10 figure