Search results for "Critical exponent"
showing 10 items of 141 documents
Dynamics of Dense Polymers: A Molecular Dynamics Approach
1988
The physics of polymeric materials[1, 2] is one of the most challenging problems in condensed matter physics today. It is a problem of great interest both from a fundamental viewpoint and for their various technical applications. In addition to theortical and experimental approaches, computer simulations[3–11] have played an important role in our present understanding of polymers. For static properties Monte Carlo methods have been widely used and give excellent results for static critical exponents. To investigate dynamic properties three different methods — Monte Carlo (MC)[3–7], molecular dynamics (MD)[8, 9] and Brownian dynamics methods[10] — have been used. Detailed microscopic dynamic…
Universality classes for wetting in two-dimensional random-bond systems
1991
Interface-unbinding transitions, such as those arising in wetting phenomena, are studied in two-dimensional systems with quenched random impurities and general interactions. Three distinct universality classes or scaling regimes are investigated using scaling arguments and extensive transfer-matrix calculations. Both the critical exponents and the critical amplitudes are determined for the weak- and the strong-fluctuation regime. In the borderline case of the intermediate-fluctuation regime, the asymptotic regime is not accessible to numerical simulations. We also find strong evidence for a nontrivial delocalization transition of an interface that is pinned to a line of defects.
How Universal is the Scaling Theory of Localization?
1991
The numerical implementation of the one-parameter scaling theory of localization is reviewed for the Anderson model of disordered solids. A finite-size scaling procedure is used to derive the 3D localization length and d.c.-conductivity from the raw data computed for quasi-1D systems by the strip-and-bar method. While a common scaling function can be unambiguously obtained for different distributions of the diagonal disorder in the Anderson model, discrepancies appear between the box and the Gaussian distribution with regard to the derived critical exponents. To discuss these effects, new results are presented for a triangular distribution, and a new method for the computation of the critic…
Specific features of the interfacial tension in the case of phase separated solutions of random copolymers
2000
Abstract Phase diagrams (cloud point curves, critical points, tie lines for constant critical composition) and interfacial tensions as a function of temperature were measured for solutions of two random copolymers: poly(dimethylsiloxane- ran -methylphenylsiloxane) [I] and poly(styrene- ran -acrylonitrile) [II]. Acetone and anisole served as solvents for I and toluene for II; all solutions exhibit UCSTs between 300 and 310 K. The phase separation behavior can be well modeled if one accounts for the molecular and chemical non-uniformities of the random copolymers used in this study. The interfacial tensions σ differ most markedly from that of comparable homopolymer solutions in their correlat…
Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
1984
Abstract In this paper we study the existence of nontrivial solutions for the boundary value problem { − Δ u − λ u − u | u | 2 ⁎ − 2 = 0 in Ω u = 0 on ∂ Ω when Ω⊂Rn is a bounded domain, n ⩾ 3, 2 ⁎ = 2 n ( n − 2 ) is the critical exponent for the Sobolev embedding H 0 1 ( Ω ) ⊂ L p ( Ω ) , λ is a real parameter. We prove that there is bifurcation from any eigenvalue λj of − Δ and we give an estimate of the left neighbourhoods ] λ j ⁎ , λj] of λj, j∈N, in which the bifurcation branch can be extended. Moreover we prove that, if λ ∈ ] λ j ⁎ , λj[, the number of nontrivial solutions is at least twice the multiplicity of λj. The same kind of results holds also when Ω is a compact Riemannian manif…
Nonequilibrium critical scaling in quantum thermodynamics
2016
The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully …
Scaling of Berry's phase close to the Dicke quantum phase transition
2006
We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading order in the 1/N expansion of the Berry phase and its critical exponent.
Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition
2011
We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the…
Finite-size scaling in Ising-like systems with quenched random fields: Evidence of hyperscaling violation
2010
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard formulations of finite size scaling near critical points break down. In this work, the consequences of modified hyperscaling are analyzed in detail. The most striking outcome is that the free energy cost \Delta F of interface formation at the critical point is no longer a universal constant, but instead increases as a power law with system size, \Delta F proportional to $L^\theta$, with $\theta$ the violation of hyperscaling critical exponent, and L the linear ex…
Specific heat studies of ortho-deuterium monolayers physisorbed on graphite
1986
The specific heat of ortho-deuterium monolayers physisorbed on graphite (Grafoil) has been studied in detail at about 100 coverages in the total density range below monolayer completion and at temperatures between 2 and 40 K. Several interesting new features were observed: At the completion of the commensurate 3 × 33 R30° phase the system undergoes an order-disorder transition at T = 18.1 K. This temperature turns out to be 2.34 K lower than that of para-hydrogen on graphite, which elucidates the significant influence of the quantum zero-point energy on these systems. From the heat-capacity data a value of 0.31 ± 0.02 is deduced for the critical exponent a which is in good agreement with th…