Search results for "Critical dimension"

Concentration and energy fluctuations in a critical polymer mixture

1995

A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the concentration distribution, the coexistence curve separating the A-rich and B-rich phases is identified as a function of temperature and chemical potential. To locate the critical point of the model, the cumulant intersection method is used. The accuracy of this approach for determining the critical parameters of fluids is assessed. Attention is then focused on the joint distribution function of the critical concentration and energy, which is analysed usi…

Critical behavior of short range Potts glasses

1993

We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short rangep=3 state Potts glass model in dimensionsd=2,3,4 with both Gaussian and bimodal (±J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. Ind=2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states forp=3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase atT=0 ind=2 with an algebraic singularity, aT=0 transition ind=3 with an essential singularity of the form χ∼exp(const.T−2), and an algebraic singularity atT…

Understanding Acid Reaction and Diffusion in Chemically Amplified Photoresists: An Approach at the Molecular Level

2011

Acid diffusion in chemically amplified resist might limit the ultimate minimum half-pitch that can be achieved with high sensitivity resists unless diffusion length is reduced until new methods of sensitizing resists are found. Precise knowledge of molecular dynamics of resist materials and advanced techniques need to be developed actively for this issue. In this sense, computer simulations have become a valuable tool in terms of reducing time and costs. However, simulations are generally based on continuum or mesoscale models, which are unable to accurately predict variations at the molecular level. Deeper understanding and investigation of the coupled reaction-diffusion kinetics at the mo…

Computer simulation of models for orientational glasses

1991

Abstract Monte Carlo studies of two- and three-dimensional lattice models where quadrupoles interact with a nearest-neighbor Gaussian coupling are reviewed. None of these models has a thermodynamic glass phase transition at non-zero temperature like the Ising spin glass: rather, phase transitions at zero temperature occur that exhibit a dynamical freeze-in spread out over a wide temperature range and are characterized by a strongly non-exponential relaxation. The time-dependent glass order parameter, q(t), decays with time, t, compatible with a stretched exponential decay q(t) ∼ exp [− (t/τ)y] with a strongly temperature-dependent exponent. While the static glass ‘susceptibility’ for isotro…

The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents

2004

The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, $$, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions $D > 2$ one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes…

Complex-mass renormalization in chiral effective field theory

2009

We consider a low-energy effective field theory of vector mesons and Goldstone bosons using the complex-mass renormalization. As an application we calculate the mass and the width of the $\rho$ meson.

Interface localization transition in Ising films with competing walls: Ginzburg criterion and crossover scaling.

1996

Dimensionality Dependence of the Metal-Insulator Transition in the Anderson Model of Localization

1996

The metal-insulator transition is investigated by means of the transfer-matrix method to describe the critical behavior close to the lower critical dimension 2. We study several bifractal systems with fractal dimensions between 2 and 3. Together with 3D and 4D results, these data give a coherent description of the dimensionality dependence of the critical disorder and the critical exponent in terms of the spectral dimension of the samples. We also show that the upper critical dimension is probably infinite, certainly larger than 4.

Ising Spin-Glass on a Lattice with Small Loops

1991

We consider the Ising spin-glass on a special lattice containing small loops with finite coordination number c. We derive the equation for the effective field distribution. With zero external field, we calculate the spin-glass transition temperature and obtain the lower critical dimension of the system. We investigate the system near and below the spin-glass transition and find that the replica symmetric solution is unstable in the low-temperature phase. Our results indicate that the replica symmetry breaking (RSB) effects are stronger than that of the Bethe lattice and furthermore, RSB is enhanced as the dimension (c/2) is decreased. Comparison with recent results of the 1/d expansion is a…

Spin stiffness of vector spin glasses

2011

Abstract We study domain-wall excitations for O ( m ) vector spin glasses in the limit m → ∞ , where the energy landscape is simplified considerably compared to XY or Heisenberg models due to the complete disappearance of metastability. Using numerical ground-state calculations and appropriate pairs of complementary boundary conditions, domain-wall defects are inserted into the systems and their excitation energies are measured. This allows us to determine the stiffness exponents for lattices of a range of spatial dimensions d = 2 , … , 7 . Compiling these results, we can finally determine the lower critical dimension of the model. The outcome is compared to estimates resulting from field-t…