The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a variety of other spin systems generally assumed to belong to the same critical universality class. In particular, we have also derived the analogous expansions for the Ising models with spin s=1,3/2,.. and for the lattice euclidean scalar field theory with quartic self-interaction, on the simple cubic and the body-centered cubic lattices. Our bivariate high-temperature expansions, which extend through K^24, enable us to compute, through the same order, all higher derivatives of the free energy with respect to the field, namely all higher susceptibilities. These data make more accurate checks possible, in critical conditions, both of the scaling and the universality properties with respect to the lattice and the interaction structure and also help to improve an approximate parametric representation of the critical equation of state for the three-dimensional Ising model universality class.Comment: 22 pages, 10 figure

Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices

High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude-ratios which determine the critical equation of state. We have obtained a substantial extension through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s >= 1/2 and for the lattice scalar field theory with quartic self-interaction, on the simple-cubic and the body-centered-cubic lattices in four, five and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions, yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.Comment: 17 pages, 10 figure

Origin of Native Driving Force in Protein Folding

We derive an expression with four adjustable parameters that reproduces well the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein structures. The numerical values of the parameters can be approximately computed from the surface tension of water, water-screened dipole interactions between residues and water and among residues, and average exposures of residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table

Theory of NMR as a local probe for the electronic structure in the mixed state of the high-TcT_c cuprates

We argue that nuclear magnetic resonance experiments are a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. Within a spin-fermion model, we show that the Doppler-shifted electronic spectrum arising from the circulating supercurrent changes the low-frequency behavior of the imaginary part of the spin-susceptibility. For a hexagonal vortex lattice, we predict that these changes lead to {\it (a)} a unique dependence of the $^{63}$Cu spin lattice relaxation rate, $1/T_1$, on resonance frequency, and {\it (b)} a temperature dependence of $T_1$ which varies with frequency. We propose a nuclear quadrupole experiment to study the effects of a uniform supercurrent on the electronic structure and predict that $T_1$ varies with the direction of the supercurrent.Comment: RevTex, 5 pages, 3 figures embedded in the tex

Solitary Waves of Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect

A branch of uniformly-propagating solitary waves of planar ferromagnets is identified. The energy dispersion and structures of the solitary waves are determined for an isotropic ferromagnet as functions of a conserved momentum. With increasing momentum, their structure undergoes a transition from a form ressembling a droplet of spin-waves to a Skyrmion/anti-Skyrmion pair. An instability to the formation of these solitary waves is shown to provide a mechanism for the electric field-induced breakdown of the spin-polarized quantum Hall effect.Comment: 5 pages, 3 eps-figures, revtex with epsf.tex and multicol.st

Dirac quasiparticles in the mixed state

Energies and wave functions are calculated for d-wave quasiparticles in the mixed state using the formalism of Franz and Tesanovic for the low-lying energy levels. The accuracy of the plane-wave expansion is explored by comparing approximate to exact results for a simplified one-dimensional problem, and the convergence of the plane- wave expansion to the two-dimensional case is studied. The results are used to calculate the low-energy tunneling density of states and the low-temperature specific heat, and these theoretical results are compared to semiclassical treatments and to the available data. Implications for the muon spin resonance measurements of vortex core size are also discussed.Comment: 13 pages, 15 figures, RevTeX. References corrected. A factor of 2 in the results has been corrected, and the conclusions have been update

Reconstructed Rough Growing Interfaces; Ridgeline Trapping of Domain Walls

We investigate whether surface reconstruction order exists in stationary growing states, at all length scales or only below a crossover length, $l_{\rm rec}$. The later would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature they evolve in a layer-by-layer mode within a crossover length scale $l_{\rm R}$, but are always rough at large length scales. We investigate this issue in the context of KPZ type dynamics and a checker board type reconstruction, using the restricted solid-on-solid model with negative mono-atomic step energies. This is a topology where surface reconstruction order is compatible with surface roughness and where a so-called reconstructed rough phase exists in equilibrium. We find that during growth, reconstruction order is absent in the thermodynamic limit, but exists below a crossover length $l_{\rm rec}>l_{\rm R}$, and that this local order fluctuates critically. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics

Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence

We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of grain sizes different from isotropic theories. As an application of our results, we show that the persistence decay exponent depends on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure

Quasiparticle excitation in and around the vortex core of underdoped YBa_2Cu_4O_8 studied by site-selective NMR

We report a site-selective ^{17}O spin-lattice relaxation rate T_1^{-1} in the vortex state of underdoped YBa_2Cu_4O_8. We found that T_1^{-1} at the planar sites exhibits an unusual nonmonotonic NMR frequency dependence. In the region well outside the vortex core, T_1^{-1} cannot be simply explained by the density of states of the Doppler-shifted quasiparticles in the d-wave superconductor. Based on T_1^{-1} in the vortex core region, we establish strong evidence that the local density of states within the vortex core is strongly reduced.Comment: 5 pages, 3 figure

Surface Critical Phenomena and Scaling in the Eight-Vertex Model

We give a physical interpretation of the entries of the reflection $K$-matrices of Baxter's eight-vertex model in terms of an Ising interaction at an open boundary. Although the model still defies an exact solution we nevertheless obtain the exact surface free energy from a crossing-unitarity relation. The singular part of the surface energy is described by the critical exponents $\alpha_s = 2 - \frac{\pi}{2\mu}$ and $\alpha_1 = 1 - \frac{\pi}{\mu}$, where $\mu$ controls the strength of the four-spin interaction. These values reduce to the known Ising exponents at the decoupling point $\mu=\pi/2$ and confirm the scaling relations $\alpha_s = \alpha_b + \nu$ and $\alpha_1 = \alpha_b -1$.Comment: 12 pages, LaTeX with REVTEX macros needed. To appear in Physical Review Letter