An exact one-particle-irreducible renormalization-group generator for critical phenomena

An exact one-particle-irreducible renormalization-group generator for critical phenomena is derived by an infinitesimal saddle-point expansion. This replaces the usual field-theoretic loop-expansion for the free energy and Green's functions with an explicit differential equation.     

A density-matrix approach to critical phenomena

A density-matrix approach to the constrained Hartree-Fock problem is proposed as an alternative to Kümmel's maximum overlap method for the study of critical phenomena, with reference to two different quasi-spin models. Excellent results are obtained.     

Phase slip phenomena in superconductors: from ordered to chaotic dynamics

We consider flux penetration to a 2D superconducting cylinder. We show that in the low field limit the kinetics is deterministic. In the strong field limit the dynamics becomes stochastic. Surprisingly the inhomogeneity in the cylinder reduces the level of stochasticity because of the predominance of Kelvin-Helmholtz vortices.     

Entanglement in quantum critical phenomena

Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of entanglement in spin chain systems, both near and at a quantum critical point. Our results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories. We explore some of the implications of this connection.     

Resonance phenomena and long-term chaotic advection in volume-preserving systems

Creating chaotic advection is the most efficient strategy to achieve mixing on microscale or in very viscous fluids. In this paper, we present a quantitative theory of the long-time resonant mixing in 3D near-integrable flows. We use the flow between two coaxial elliptic counter-rotating cylinders as a demonstrative model, where multiple scatterings on resonance result in mixing by causing the jumps of adiabatic invariants. We improve the existing estimates of the width of the mixing domain. We show that the resulting mixing both on short and long time scales can be described in terms of a single diffusion-type equation with a diffusion coefficient depending on the averaged effect of multiple passages through resonances. We discuss the exact location of the boundaries of the chaotic domain and show how it affects the properties of mixing.     

Field-theoretical approach to static critical phenomena in semi-infinite systems

The critical behaviour of a semi-infinite system withO(n) spin symmetry is studied in 4- dimensions near the ordinary transition using renormalization-group methods of field theory and -expansion techniques. It is found that, to all orders in , all surface exponents can be expressed in terms of two bulk exponents and a single surface exponent which follows from the anomalous dimension of the derivative (x ,0) of The order parameter (x,x ) at the surface (x =0). As a byproduct, Barber's scaling law 2₁ – ₁₁ = + is obtained. The surface exponents are calculated to second order in . Our results show that the scaling relation = ^–1 proposed by Bray and Moore is incorrect. The behaviour of various scaling functions close to the surface (i.e. forx correlation length) is determined with the help of short-distance expansions. We also treat corrections to scaling and logarithmic corrections in four dimensions. Our results for the logarithmic corrections of the layer and local susceptibilities disagree with those obtained by Guttmann and Reeve.A brief account of some of the results presented here was given in [1]. The surface exponents were independently calculated to order ² by Reeve and Guttmann [2] using an alternative method     

Nonuniversal routes to universality: critical phenomena in colloidal dispersions

We investigate critical phenomena in colloids by means of the renormalization-group based hierarchical reference theory of fluids. We focus on three experimentally relevant model systems: namely, the Asakura-Oosawa model of a colloidal dispersion under the influence of polymer-induced attractive depletion forces; fluids with competing short-range attractive and longer-range repulsive interactions; solutions of star polymers whose pair potential presents both an attractive well and an ultrasoft repulsion at shorter distance. Our results show that the ability to tune the effective interactions between colloidal particles allows one to generate a variety of crossovers to the asymptotic critical behavior, which are not observed in atomic fluids.     

Conformal field theories and critical phenomena

In this article we present a brief review of the conformal symmetry and the two-dimensional conformal quantum field theories. As concrete applications of the conformal theories to the critical phenomena in statistical systems, we calculate the value of central charge and the anomalous scale dimensions of the Z ₂ symmetric quantum chain with boundary condition. The results are compatible with the prediction of the conformal field theories.     

Roughness-induced critical phenomena in a turbulent flow

I present empirical evidence that turbulent flows are closely analogous to critical phenomena, from a reanalysis of friction factor measurements in rough pipes. The data collapse found here corresponds to Widom scaling near critical points, and implies that a full understanding of turbulence requires explicit accounting for boundary roughness.     

Directed polymer melts and quantum critical phenomena

The statistical mechanics of directed linelike objects, such as directed polymers in an external field, strands of dipoles in both ferro- and electrorheological fluids, and flux lines in high-T_c superconductors, bears a close resemblance to the quantum mechanics of bosons in 2+1 dimensions. We show that single-component and binary mixture critical phenomena in these systems are in the universality class of three-dimensional uniaxial dipolar ferromagnets and ferroelectrics. Our results also apply to films of two superfluid species undergoing phase separation well below their -points near T=0. In the case of directed polymers and electrorheological fluids we analyze the effects of free ends occurring in the sample as well as a novel directionally-dependent compressibility.