Thermodynamics of an incommensurate quantum crystal

We present a simple theory of the thermodynamics of an incommensurate quantum solid. The ground state of the solid is assumed to be an incommensurate crystal, with quantum zero-point vacancies and interstitials and thus a non-integer number of atoms per unit cell. We show that the low temperature variation of the net vacancy concentration should be as $T^4$, and that the first correction to the specific heat due to this varies as $T^7$; these are quite consistent with experiments on solid $^4$He. We also make some observations about the recent experimental reports of ``supersolidity'' in solid $^4$He that motivate a renewed interest in quantum crystals.Comment: revised, new title, somewhat expande

Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions

We consider the effect of quenched spatial disorder on systems of interacting, pinned non-Abelian anyons as might arise in disordered Hall samples at filling fractions \nu=5/2 or \nu=12/5. In one spatial dimension, such disordered anyon models have previously been shown to exhibit a hierarchy of infinite randomness phases. Here, we address systems in two spatial dimensions and report on the behavior of Ising and Fibonacci anyons under the numerical strong-disorder renormalization group (SDRG). In order to manage the topology-dependent interactions generated during the flow, we introduce a planar approximation to the SDRG treatment. We characterize this planar approximation by studying the flow of disordered hard-core bosons and the transverse field Ising model, where it successfully reproduces the known infinite randomness critical point with exponent \psi ~ 0.43. Our main conclusion for disordered anyon models in two spatial dimensions is that systems of Ising anyons as well as systems of Fibonacci anyons do not realize infinite randomness phases, but flow back to weaker disorder under the numerical SDRG treatment.Comment: 12 pages, 12 figures, 1 tabl

Finite Size Effects in Vortex Localization

The equilibrium properties of flux lines pinned by columnar disorder are studied, using the analogy with the time evolution of a diffusing scalar density in a randomly amplifying medium. Near H_{c1}, the physical features of the vortices in the localized phase are shown to be determined by the density of states near the band edge. As a result, H_{c1} is inversely proportional to the logarithm of the sample size, and the screening length of the perpendicular magnetic field decreases with temperature. For large tilt the extended ground state turns out to wander in the plane perpendicular to the defects with exponents corresponding to a directed polymer in a random medium, and the energy difference between two competing metastable states in this case is extensive. The divergence of the effective potential associated with strong pinning centers as the tilt approaches its critical value is discussed as well.Comment: 10 pages, 2 figure

Nernst effect in the vortex-liquid regime of a type-II superconductor

We measure the transverse thermoelectric coefficient $\alpha_{xy}$ in simulations of type-II superconductors in the vortex liquid regime, using the time-dependent Ginzburg-Landau (TDGL) equation with thermal noise. Our results are in reasonably good quantitative agreement with experimental data on cuprate samples, suggesting that this simple model of superconducting fluctuations contains much of the physics behind the large Nernst effect observed in these materials.Comment: 6 pages. Expanded version of text. New Fig.

Day / night variation in fish directivity in the trawl opening

Still photographs of fish in the mouth area of a bottom trawl were taken by a downwards-oriented automated strobe camera mounted near the headrope. Fish angles relative to the towing direction were measured. Fish were significantly less polarized by night than by day, and in the daytime photographs less polarization was seen at low fish densities than at higher. The results are discussed with regard to fish herding patterns and potential escapement beneath the fishing line of a trawl

On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents

Finite-size scaling (FSS) is a standard technique for measuring scaling exponents in spin glasses. Here we present a critique of this approach, emphasizing the need for all length scales to be large compared to microscopic scales. In particular we show that the replacement, in FSS analyses, of the correlation length by its asymptotic scaling form can lead to apparently good scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page

Collinear N\'eel-type ordering in partially frustrated lattices

We consider two partially frustrated S = 1/2 antiferromagnetic spin systems on the triangular and pentagonal lattices. In an elementary plaquette of the two lattices, one bond has exchange interaction strength $\alpha$ ($\alpha \leq 1$) whereas all other bonds have exchange interaction strength unity. We show that for $\alpha$ less than a critical value $\alpha_{c}$, collinear N\'eel-type ordering is possible in the ground state. The ground state energy and the excitation spectrum have been determined using linear spin wave theory based on the Holstein-Primakoff transformation.Comment: Four pages, LaTeX, Four postscripts figures, Phys. Rev. B58, 73 (1998

Coulomb and Liquid Dimer Models in Three Dimensions

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar, correlations, in excellent agreement with our large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.Comment: 4 pages with corrections and update

Ground-State Phase Diagram of the Two-Dimensional Quantum Heisenberg Mattis Model

The two-dimensional $S=1/2$ asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The N\'eel order parameter and the spin glass order parameter can be smoothly extrapolated to the thermodynamic limit in the antiferromagnetic region, as in the pure Heisenberg antiferromagnet. The critical concentration of the N\'eel phase is consistent with that of the two-dimensional Ising Mattis model, and the spin glass order parameter increases monotonously as the ferro-bond concentration increases. These facts suggest that quantum fluctuation does not play an essential role in two-dimensional non-frustrated random spin systems. KEYWORDS: quantum spin system, ground state, randomness, Mattis model, N\'eel order, spin glass orderComment: 10 pages, LaTeX, 6 compressed/uuencoded postscript figures, J. Phys. Soc. Jpn. 65 (1996) No. 2 in pres

Ground State Structure in a Highly Disordered Spin Glass Model

We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining (infinite volume) ground states for this model can be related to invasion percolation with the number of ground states identified as $2^{\cal N}$, where ${\cal N} = {\cal N}(d)$ is the number of distinct global components in the ``invasion forest''. We prove that ${\cal N}(d) = \infty$ if the invasion connectivity function is square summable. We argue that the critical dimension separating ${\cal N} = 1$ and ${\cal N} = \infty$ is $d_c = 8$. When ${\cal N}(d) = \infty$, we consider free or periodic boundary conditions on cubes of side length $L$ and show that frustration leads to chaotic $L$ dependence with {\it all} pairs of ground states occuring as subsequence limits. We briefly discuss applications of our results to random walk problems on rugged landscapes.Comment: LaTex fil