Non-linear response to an external AC drive near the Kosterlitz Thouless phase transition

We discuss the effect of an external AC drive on the motion of vortices near the vortex unbinding transition in two-dimensional superfluids, and on the motion of the interface between a crystal and its melt at the roughening transition. Both belong to the Kosterlitz Thouless class of phase transitions. There are three length scales in the problem: the correlation length, a diffusion length which varies as and a length inversely related to the strength of the drive. A possible resonance experiment for helium crystals is discussed.     

Breakdown of one-parameter scaling in quantum critical scenarios for high-temperature copper-oxide superconductors

We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent z satisfies the unphysical constraint, z < 0. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single-correlation length scale is necessary to model transport in the cuprates.     

Non-monotonic temperature evolution of nonlocal structure–dynamics correlation in CuZr glass-forming liquids

The structure–dynamics correlations in a nonlocal manner were investigated in CuZr metallic glass-forming liquids via classical molecular dynamics simulations. A spatial coarse-graining approach was employed to incorporate the nonlocal structural information of given structural order parameters in the structure–dynamics relationship. It is found that the correlation between structure order parameters and dynamics increases with increasing coarse-graining length and has a characteristic length scale. Moreover, the characteristic correlation length exhibits a non-monotonic temperature evolution as temperature approaches glass transition temperature, which is not sensitive to the considered structure order parameters.Our results unveil a striking change in the structure–dynamics correlation, which involves no fitting theoretical interpretation. These findings provide new insight into the structure–dynamics correlation in glass transition.     

Phase and vortex correlations in superconducting Josephson-junction arrays at irrational magnetic frustration

Phase coherence and vortex order in a Josephson-junction array at irrational frustration are studied by extensive Monte Carlo simulations using the parallel-tempering method. A scaling analysis of the correlation length of phase variables in the full equilibrated system shows that the critical temperature vanishes with a power-law divergent correlation length and critical exponent nuph, in agreement with recent results from resistivity scaling analysis. A similar scaling analysis for vortex variables reveals a different critical exponent nuv, suggesting that there are two distinct correlation lengths associated with a decoupled zero-temperature phase transition.     

Finite-size effects and phase transition in the three-dimensional three-state Potts model

The three-state Potts model in three dimensions is studied by Monte Carlo and finite-size scaling techniques. Using a histogram method recently proposed by Ferrenberg and Swendsen, the finite-size dependence for the maximum of the specific heat is found to scale with the volume of the system, indicating that the phase transition is of first order. The value of the latent heat per spin and the correlation length at the transition are estimated.     

Self-consistent treatment of a phase transition

A self-consistent treatment of a phase transition with a scalar order parameter in the ordered and disordered state is described. The factorization of the correlation functions in the disordered phase leads to a shift of the transition temperature, a linear divergence (=1) for the correlation length, a quadratic divergence (=2) for the susceptibility, and a finite value (=–1) for the specific heat. In the ordered phase the factorization of the correlation functions leads to no divergences in the correlation length and susceptibility. A study of the free energy shows that order persists above the transition temperature found by assuming disorder. The requirement of thermodynamic stability induces a first-order transition at a temperature which lies between the bare transition temperature and the shifted one.Supported in part by NSF grant No-GP-17560.This work is in partial fulfillment of Ph.D. requirements at Brandeis University.     

Upper bounds on the transition temperature of classical n.n. ferromagnetic systems for general n and d

A differential equation is obtained for the spin-spin correlation function of a system of n-component classical spins interacting via a nearest neighbour ferromagnetic interaction. The differential equation makes it possible to obtain upper bounds on the correlation length and the transition temperature. It also makes it possible to relate the correlation length with the energy per spin and to obtain a necessary condition for the existence of the phase transition in terms of the energy per spin.     

Renormalisation group approach to Bose-Einstein transition

Renormalisation group approach is applied to the Bose-Einstein transition. The value obtained for the correlation length index suggests that the universality hypothesis holds irrespective of the classical or quantum nature of a phase transition.     

Freezing of random RNA

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.     

Bootstrap Percolation and Kinetically Constrained Models on Hyperbolic Lattices

We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained models, which are in turn relevant for the study of glass and jamming transitions. We show that for generic tilings there exists a BP transition at a nontrivial critical density, 0<ρ _c <1. Thus, despite the presence of loops on all length scales in hyperbolic lattices, the behavior is very different from that on Euclidean lattices where the critical density is either zero or one. Furthermore, we show that the transition has a mixed character since it is discontinuous but characterized by a diverging correlation length, similarly to what happens on Bethe lattices and random graphs of constant connectivity.     

Multipartite entanglement signature of quantum phase transitions

We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.     

Correlation functions in the multiple Ising model coupled to gravity

The model of p Ising spins coupled to 2d gravity, in the form of a sum over planar φ³ graphs, is studied and in particular the two-point and spin-spin correlation functions are considered. We first solve a toy model in which only a partial summation over spin configurations is performed and, using a modified geodesic distance, various correlation functions are determined. The two-point function has a diverging length scale associated with it. The critical exponents are calculated and it is shown that all the standard scaling relations apply. Next the full model is studied, in which all spin configurations are included. Many of the considerations for the toy model apply for the full model, which also has a diverging geometric correlation length associated with the transition to a branched polymer phase. Using a transfer function we show that the two-point and spin-spin correlation functions decay exponentially with distance. Finally, by assuming various scaling relations, we make a prediction for the critical exponents at the transition between the magnetized and branched polymer phases in the full model.     

叶栅边界层转捩的实验研究与一个新的综合经验准则

叶栅边界层转捩的实验研究与一个新的综合经验准则蒋洪德，仲永兴，凌君（中国科学院工程热物理研究所北京１０００８０）（中国航空工业总公司６２４所）关键词转捩实验，经验准则１前言现代航空发动机的风扇、压气机和涡轮叶栅在工作状态下弦长雷诺数一般在１０５～１０...     

New spin-orbit-induced universality class in the integer quantum Hall regime

Using heuristic arguments and numerical simulations it is argued that the critical exponent nu describing the localization length divergence at the integer quantum-Hall transition is modified in the presence of spin-orbit scattering with short-range correlations. The exponent is very close to nu=4/3, the percolation correlation length exponent, consistent with the prediction of a semiclassical argument. In addition, a band of weakly localized states is conjectured.     

Stability of the Haldane state against the antiferromagnetic-bond randomness

Ground-state phase diagram of the one-dimensional bond-random S=1 Heisenberg antiferromagnet is investigated by means of the loop-cluster-update quantum Monte-Carlo method. The random couplings are drawn from a rectangular uniform distribution. We found that even in the case of extremely broad bond distribution, the magnetic correlation decays exponentially, and the correlation length is hardly changed; namely, the Haldane phase continues to be realized. This result is accordant with that of the exact-diagonalization study, whereas it might contradict the conclusion of an analytic theory founded in a power-law bond distribution instead. The latter theory predicts that a second-order phase transition occurs at a certain critical randomness, and the correlation length diverges for sufficiently strong randomness. Received: 31 March 1998 / Revised and Accepted: 7 July 1998     

Influence of correlated impurities on the onset of cooper pairing

Effect of two-particle correlations between impurities on the temperature of transition of a Fermi liquid in the superfluid or superconducting state is analyzed. It is shown, that correlations with a radius, exceeding correlation length of the superconductor can have a pronounced effect on the transition temperature. The equation for the transition temperature is corrected for correlations of the impurities. Possible applications of the new equation are discussed.     

Correlation length and fluctuations in inhomogeneous superconductors

The correlation length and the effect of fluctuations of the grains are calculated for weakly coupled granular superconductors, using a two order parameter Ginzburg-Landau-Wilson functional. The main effect of fluctuations is shown to be a shift of the coherent transition temperature, and the correlation length is compared to the corresponding expression in strongly coupled granular superconductors.     

Single spin and chiral glass transition in vector spin glasses in three dimensions

Results of Monte Carlo simulations of XY and Heisenberg spin glass models in three dimensions are presented. A finite-size scaling analysis of the correlation length of the spins and chiralities of both models shows that there is a single, finite-temperature transition at which both spins and chiralities order.     

Viscosity of a liquid crystal near the nematic-smectic A phase transition

We report the results of an x-ray scattering study where both the dynamic and the static properties of a liquid crystal (8OCB) near the nematic-smectic A phase transition were probed. The static, time-averaged data show the gradual formation of smectic layers in the nematic phase, and we find that the smectic order correlation length parallel to the molecular axis diverges with the critical exponent nu( parallel )=0.70(4) at the transition. The literature value is nu( perpendicular )=0.58 for the perpendicular direction. By x-ray photon correlation spectroscopy, we find that the viscosity coefficient eta(3) shows critical, diverging behavior at the phase transition with a critical exponent x=0.95(5). This contradicts previous light scattering work (x=0.50), but is in good agreement with the theoretical prediction x=3nu( parallel )-2nu( perpendicular ) by Hossain et al.     

Non-locally correlated disorder and delocalization in one dimension (II). Localization length

We study the delocalization transition in a one-dimensional Dirac fermion system with randomly varying mass by using supersymmetric (SUSY) methods. In a previous paper, we calculated density of states and found that (quasi-) extended states near the band center are enhanced by non-local correlation of the random Dirac mass. Numerical studies support this conclusion. In this paper, we calculate the localization length as a function of the correlation length of the disorder. The result shows that the localization length is an increasing function of the correlation of the random mass.