Search results for " Exponent"
showing 10 items of 315 documents
The mean field to Ising crossover in the critical behavior of polymer mixtures : a finite size scaling analysis of Monte Carlo simulations
1993
Monte Carlo simulations of the bond fluctuation model of symmetrical polymer mixtures (chain lengths N A =N B =N) are analyzed near the critical temperature T c (N) of their unmixing transition. Two choices of interaction range are studied, using a square-well potential with effective coordination number z eff ≃ 14 or z eff ≃ 5, respectively, at a volume fraction O= 0.5 of occupied lattice sites, and chain lengths in the range 8≤ N≤ 512. A linear relation between N and T c (N) is established, T c (N)= AN+B, where the correction term B is positive for z eff = 14 but negative for z eff = 5. The critical behavior of the models is analyzed via finite size scaling techniques, paying attention to…
Critical phenomena in polymer mixtures: Monte Carlo simulation of a lattice model
1987
A lattice model of a symmetrical binary (AB) polymer mixture is studied, modelling the polymer chains by self-avoiding walks withN A =N B =N steps on a simple cubic lattice. If a pair of nearest neighbour sites is taken by different monomersAB orBA, an energye ab is won; if the pair of sites is taken by anAA or aBB pair, an energye is won, while the energy is reduced to zero if at least one of the sites of the pair is vacant. To allow enough chain mobility, 20% of the lattice sites are vacancies. In addition to local motions of the chain segments we use a novel “grand-canonical” simulation technique:A chains are transformed intoB chains and vice versa, keeping the chemical potential differe…
Domain-wall excitations in the two-dimensional Ising spin glass
2018
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to $10\,000\times 10\,000$ spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic…
Spin-one-Ising model for (CO)1?x (N2) x mixtures: A finite size scaling study of random-field-type critical phenomena
1995
A qualitative model for solid mixtures of diatomic molecules, where one species (called CO, to be specific) carries both a dipole moment and a quadrupole moment, while the other species (calledN 2) has only a quadrupole moment, is studied by Monte Carlo methods. We use spinsS i =±1 to represent the orientations of the CO electric dipole moment, if the lattice sitei is taken by a CO molecule, whileS i =0 if the site is taken by anN 2 molecule. Assuming nearest-neighbor antiferroelectric interactions between CO molecules, and a bilinear dipole-quadrupole coupling between CO andN 2, the randomly quenchedN 2 molecules act like random fields do in the random field Ising model. In previous work i…
Renormalization-scheme ambiguity and perturbation theory near a fixed point
1984
We consider the perturbative calculation of critical exponents in massless, renormalizable theories having a nontrivial fixed point. In conventional perturbation theory, all results depend on the arbitrary renormalization scheme used. We show how to resolve this problem, following the "principle of minimal sensitivity" approach. At least three orders of perturbation theory are required for quantitative results. We give scheme-independent criteria for determining the presence or absence of a fixed point in $n\mathrm{th}$ order, and discuss the conditions under which perturbative results might be reliable. As illustrations we discuss QED with many flavors, and ${({\ensuremath{\varphi}}^{4})}_…
Wilsonʼs momentum shell renormalization group from Fourier Monte Carlo simulations
2011
Abstract Previous attempts to accurately compute critical exponents from Wilsonʼs momentum shell renormalization prescription suffered from the difficulties posed by the presence of an infinite number of irrelevant couplings. Taking the example of the 1d long-ranged Ising model , we calculate the momentum shell renormalization flow in the plane spanned by the coupling constants ( u 0 , r 0 ) for different values of the momentum shell thickness parameter b by simulation using our recently developed Fourier Monte Carlo algorithm. We report strong anomalies in the b-dependence of the fixed point couplings and the resulting exponents y τ and ω in the vicinity of a shell parameter b ⁎ 1 characte…
Electrons on a spherical surface: Physical properties and hollow spherical clusters
2012
We discuss the physical properties of a noninteracting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential, and its electric static polarizability. All these properties are discussed analytically as functions of the number $N$ of electrons. The trends obtained with increasing $N$ are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic n…
Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model
2013
AbstractThe singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other — to the maximum of CV, provide consistent values of C0 in the ansatz CV(L)=C0+ALα/ν at large L, if α/ν=0.196(6). However, a direct estimation from our data suggests that α/ν, most probably, has a smaller value (e.g., α/ν= 0.113(30)). Thus, the conventional power-law scaling ansatz can be questioned because of this inconsistency. We have found that the data are well described by certain logarithmic ansatz.
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.
High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices
1999
We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings \(\). In these star-graph expansions up to order 22 in the inverse temperature \(\), the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling Kc and the critical exponent \(\) of the spin-glass susceptibility in a large region of …