Spin-Singlet to Spin Polarized Phase Transition at ν=2/3\nu=2/3: Flux-Trading in Action

We analyze the phase transition between spin-singlet and spin-polarized states which occurs at $\nu=2/3$. The basic strategy is to use adiabatic flux-trading arguments to relate this transition to the analogous transition at $\nu=2$. The transition is found to be similar to a transition in ferromagnets. In our analysis, we find two possible scenarios. In one, the transition is first-order, in agreement with experimental and numerical studies of the $\nu=2/3$ transition. In the other, we find a second-order transition to a partially polarized state followed by a second-order transition to a fully polarized state. This picture is in qualitative agreement with experiments on the $\nu=4/3$ state, the particle-hole conjugate of $\nu=2/3$. We analyze the edge modes which propagate at the boundaries between regions of different phases and show that these do not support gapless excitations. Finally, we consider the possibility of a finite-temperature compressible state with a Fermi surface which would explain the non-zero $\rho_{xx}$ seen in experiments.Comment: 18 pages, no figures, Phyzz

Behaviour of the energy gap near a commensurate-incommensurate transition in double layer quantum Hall systems at nu=1

The charged excitations in the system of the title are vortex-antivortex pairs in the spin-texture described in the theory by Yang et al which, in the commensurate phase, are bound together by a ``string''. It is shown that their excitation energy drops as the string lengthens as the parallel magnetic field approaches the critical value, then goes up again in the incommensurate phase. This produces a sharp downward cusp at the critical point. An alternative description based on the role of disorder in the tunnelling and which appears not to produce a minimum in the excitation energy is also discussed. It is suggested that a similar transition could also occur in compressible Fermi-liquid-like states.Comment: latex file, 17 page

Quantum Hall States of High Symmetry

We identify some hidden symmetries of Chern-Simons theories, such as appear in the effective theory for quantized Hall states. This allows us to determine which filling fractions admit spin-singlet quantum Hall states. Our results shed some light on states already observed at $\nu=2/3$, and transitions between them. We identify SU(2), or higher, symmetries of many additional states -- including spin-polarized states. Our symmetries classify low-lying excited states and may be of use in the construction of trial wavefunctions, but are typically not present in the edge theory, where they are lifted by non-universal couplings.Comment: 17 pages, PostScript, 1 figure included. Revision - corrected slight error in equation (3.5) on Page

Dynamic surface scaling behavior of isotropic Heisenberg ferromagnets

The effects of free surfaces on the dynamic critical behavior of isotropic Heisenberg ferromagnets are studied via phenomenological scaling theory, field-theoretic renormalization group tools, and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed, the boundary terms of the associated dynamic field theory are identified, its renormalization in d <= 6 dimensions is clarified, and the boundary conditions it satisfies are given. Scaling laws are derived which relate the critical indices of the dynamic and static infrared singularities of surface quantities to familiar static bulk and surface exponents. Accurate computer-simulation data are presented for the dynamic surface structure factor; these are in conformity with the predicted scaling behavior and could be checked by appropriate scattering experiments.Comment: 9 pages, 2 figure

Non-Fermi Liquid Fixed Point in 2+1 Dimensions

We construct models of excitations about a Fermi surface that display calculable deviations from Fermi liquid behavior in the low-energy limit. They arise as a consequence of coupling to a Chern-Simons gauge field, whose fluctations are controlled through a ${1\over{k^x}}$ interaction. The Fermi liquid fixed point is shown to be unstable in the infrared for $x<1$, and an infrared-stable fixed point is found in a $(1-x)$-expansion, analogous to the $\epsilon$-expansion of critical phenomena. $x=1$ corresponds to Coulomb interactions, and in this case we find a logarithmic approach to zero coupling. We describe the low-energy behavior of metals in the universality class of the new fixed point, and discuss its possible application to the compressible $\nu={1\over2}$ quantum Hall state and to the normal state of copper-oxide superconductors.Comment: 24 pages, 2 figures uuencoded at end, use Phyzzx and epsf, PUPT 1438, IASSNS-HEP 93/8

Quantum Numbers of Textured Hall Effect Quasiparticles

We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.Comment: 13 pages, no figures, Phyzz

Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition

In QCD with two flavors of massless quarks, the chiral phase transition is plausibly in the same universality class as the classical four component Heisenberg antiferromagnet. Therefore, renormalization group techniques developed in the study of phase transitions can be applied to calculate the critical exponents which characterize the scaling behaviour of universal quantities near the critical point. This approach to the QCD phase transition has implications both for lattice gauge theory and for heavy ion collisions. Future lattice simulations with longer correlation lengths will be able to measure the various exponents and the equation of state for the order parameter as a function of temperature and quark mass which we describe. In a heavy ion collision, the consequence of a long correlation length would be large fluctuations in the number ratio of neutral to charged pions. Unfortunately, we show that this phenomenon will not occur if the plasma stays close to equilibrium as it cools. If the transition is far out of equilibrium and can be modelled as a quench, it is possible that large volumes of the plasma with the pion field correlated will develop, with dramatic phenomenological consequences. }Comment: phyzzx, 41 pages, 4 figures available as a postscript file from K.R., PUPT-1347, IASSNS-HEP-92/6

Spin dynamics simulations of the magnetic dynamics of RbMnF3_3 and direct comparison with experiment

Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L\leq 60$. This system is widely recognized as an appropriate model for the magnetic properties of RbMnF$_3$. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm implemented by Krech {\it etal}, which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\pm 0.03)$, which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF$_3$ are presented.Comment: 30 pages, RevTex, 9 figures, to appear in PR

Singularity in the boundary resistance between superfluid 4^4He and a solid surface

We report new measurements in four cells of the thermal boundary resistance $R$ between copper and $^4$He below but near the superfluid-transition temperature $T_\lambda$. For $10^{-7} \leq t \equiv 1 - T/T_\lambda \leq 10^{-4}$ fits of $R = R_0 t^{x_b} + B_0$ to the data yielded $x_b \simeq 0.18$, whereas a fit to theoretical values based on the renormalization-group theory yielded $x_b = 0.23$. Alternatively, a good fit of the theory to the data could be obtained if the {\it amplitude} of the prediction was reduced by a factor close to two. The results raise the question whether the boundary conditions used in the theory should be modified.Comment: 4 pages, 4 figures, revte

Hamiltonian theory of gaps, masses and polarization in quantum Hall states: full disclosure

I furnish details of the hamiltonian theory of the FQHE developed with Murthy for the infrared, which I subsequently extended to all distances and apply it to Jain fractions \nu = p/(2ps + 1). The explicit operator description in terms of the CF allows one to answer quantitative and qualitative issues, some of which cannot even be posed otherwise. I compute activation gaps for several potentials, exhibit their particle hole symmetry, the profiles of charge density in states with a quasiparticles or hole, (all in closed form) and compare to results from trial wavefunctions and exact diagonalization. The Hartree-Fock approximation is used since much of the nonperturbative physics is built in at tree level. I compare the gaps to experiment and comment on the rough equality of normalized masses near half and quarter filling. I compute the critical fields at which the Hall system will jump from one quantized value of polarization to another, and the polarization and relaxation rates for half filling as a function of temperature and propose a Korringa like law. After providing some plausibility arguments, I explore the possibility of describing several magnetic phenomena in dirty systems with an effective potential, by extracting a free parameter describing the potential from one data point and then using it to predict all the others from that sample. This works to the accuracy typical of this theory (10 -20 percent). I explain why the CF behaves like free particle in some magnetic experiments when it is not, what exactly the CF is made of, what one means by its dipole moment, and how the comparison of theory to experiment must be modified to fit the peculiarities of the quantized Hall problem