Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation length exponent we get $\nu=0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We compute the first three terms in the formal asymptotic expansion of (lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching conjecture is satisfied for (lambda_d)(p).Comment: 15 pages, much more about d=1,2,

Quantum phase transition of condensed bosons in optical lattices

In this paper we study the superfluid-Mott-insulator phase transition of ultracold dilute gas of bosonic atoms in an optical lattice by means of Green function method and Bogliubov transformation as well. The superfluid- Mott-insulator phase transition condition is determined by the energy-band structure with an obvious interpretation of the transition mechanism. Moreover the superfluid phase is explained explicitly from the energy spectrum derived in terms of Bogliubov approach.Comment: 13 pages, 1 figure

The types of Mott insulator

There are two classes of Mott insulators in nature, distinguished by their responses to weak doping. With increasing chemical potential, Type I Mott insulators undergo a first order phase transition from the undoped to the doped phase. In the presence of long-range Coulomb interactions, this leads to an inhomogeneous state exhibiting ``micro-phase separation.'' In contrast, in Type II Mott insulators charges go in continuously above a critical chemical potential. We show that if the insulating state has a broken symmetry, this increases the likelihood that it will be Type I. There exists a close analogy between these two types of Mott insulators and the familiar Type I and Type II superconductors

Algebraic Self-Similar Renormalization in Theory of Critical Phenomena

We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several different examples. The advantage of the method is in combining simplicity with high accuracy.Comment: 1 file, 44 pages, RevTe

Probing Bogoliubov Quasiparticles in Superfluid 3He with a ‘Vibrating-Wire Like’ MEMS Device

International audienceWe have measured the interaction between superfluid 3 He-B and a micro-machined goalpost-shaped device at temperatures below 0.2 T c. The measured damping follows well the theory developed for vibrating wires, in which the An-dreev reflection of quasiparticles in the flow field around the moving structure leads to a nonlinear frictional force. At low velocities the damping force is proportional to velocity while it tends to saturate for larger excitations. Above a velocity of 2.6 mms −1 the damping abruptly increases, which is interpreted in terms of Cooper-pair breaking. Interestingly, this critical velocity is significantly lower than reported with other mechanical probes immersed in superfluid 3 He. Furthermore , we report on a nonlinear resonance shape for large motion amplitudes that we interpret as an inertial effect due to quasiparticle friction, but other mechanisms could possibly be invoked as well. PACS numbers: 85.85.+j, 67.30.H-, 67.30.e

The dynamics of vortex generation in superfluid 3He-B

A profound change occurs in the stability of quantized vortices in externally applied flow of superfluid 3He-B at temperatures ~ 0.6 Tc, owing to the rapidly decreasing damping in vortex motion with decreasing temperature. At low damping an evolving vortex may become unstable and generate a new independent vortex loop. This single-vortex instability is the generic precursor to turbulence. We investigate the instability with non-invasive NMR measurements on a rotating cylindrical sample in the intermediate temperature regime (0.3 - 0.6) Tc. From comparisons with numerical calculations we interpret that the instability occurs at the container wall, when the vortex end moves along the wall in applied flow.Comment: revised & extended version. Journal of Low Temperature Physics, accepted (2008

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

NMR and NQR Fluctuation Effects in Layered Superconductors

We study the effect of thermal fluctuations of the s-wave order parameter of a quasi two dimensional superconductor on the nuclear spin relaxation rate near the transition temperature Tc. We consider both the effects of the amplitude fluctuations and the Berezinskii-Kosterlitz-Thouless (BKT) phase fluctuations in weakly coupled layered superconductors. In the treatment of the amplitude fluctuations we employ the Gaussian approximation and evaluate the longitudinal relaxation rate 1/T1 for a clean s-wave superconductor, with and without pair breaking effects, using the static pair fluctuation propagator D. The increase in 1/T1 due to pair breaking in D is overcompensated by the decrease arising from the single particle Green's functions. The result is a strong effect on 1/T1 for even a small amount of pair breaking. The phase fluctuations are described in terms of dynamical BKT excitations in the form of pancake vortex-antivortex (VA) pairs. We calculate the effect of the magnetic field fluctuations caused by the translational motion of VA excitations on 1/T1 and on the transverse relaxation rate 1/T2 on both sides of the BKT transitation temperature T(BKT)<Tc. The results for the NQR relaxation rates depend strongly on the diffusion constant that governs the motion of free and bound vortices as well as the annihilation of VA pairs. We discuss the relaxation rates for real multilayer systems where the diffusion constant can be small and thus increase the lifetime of a VA pair, leading to an enhancement of the rates. We also discuss in some detail the experimental feasibility of observing the effects of amplitude fluctuations in layered s-wave superconductors such as the dichalcogenides and the effects of phase fluctuations in s- or d-wave superconductors such as the layered cuprates.Comment: 38 pages, 12 figure