Critical behavior of the three-dimensional random-anisotropy Heisenberg model.

We have studied the critical properties of the three-dimensional random anisotropy Heisenberg model by means of numerical simulations using the Parallel Tempering method. We have simulated the model with two different disorder distributions, cubic and isotropic ones, with two different anisotropy strengths for each disorder class. For the case of the anisotropic disorder, we have found evidence of universality by finding critical exponents and universal dimensionless ratios independent of the strength of the disorder.

Shape analysis of random polymer networks.

We propose the model of a random polymer network, formed on the base on Erdös-Rényi random graph. In the language of mathematical graphs, the chemical bonds between monomers can be treated as vertices, and their chemical functionalities as degrees of these vertices. We consider graphs with fixed number of vertices= 5 and variable parameter(connectedness), defining the total number of links=(- 1)/2 between vertices.

Universal shape characteristics for the mesoscopic star-shaped polymer via dissipative particle dynamics simulations.

In this paper we study the shape characteristics of star-like polymers in various solvent quality using a mesoscopic level of modeling. The dissipative particle dynamics simulations are performed for the homogeneous and four different heterogeneous star polymers with the same molecular weight. We analyse the gyration radius and asphericity at the poor, good and θ-solvent regimes.

Universal shape characteristics for the mesoscopic polymer chain via dissipative particle dynamics.

In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in 3D space at a range of chain lengths N. The scaling laws for the end-to-end distance and gyration radius are examined first and found to hold for [Formula: see text] yielding a reasonably accurate value for the Flory exponent ν.

Monte Carlo study of anisotropic scaling generated by disorder.

We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length ξ(∥) in the direction along defects and a perpendicular correlation length ξ(⊥) in the direction perpendicular to the lines. Both ξ(∥) and ξ(⊥) diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents ν(∥) and ν(⊥) take different values.

Field theory of bicritical and tetracritical points. IV. Critical dynamics including reversible terms.

This article concludes a series of papers [Folk, Holovatch, and Moser, Phys. Rev. E 78, 041124 (2008); 78, 041125 (2008); 79, 031109 (2009)] where the tools of the field theoretical renormalization group were employed to explain and quantitatively describe different types of static and dynamic behavior in the vicinity of multicritical points.

Entropic equation of state and scaling functions near the critical point in uncorrelated scale-free networks.

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions, which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in uncorrelated scale-free networks, where the node-degree distribution exponent λ appears to be a global variable and plays a crucial role, similar to the dimensionality d for systems on lattices.

Star copolymers in porous environments: scaling and its manifestations.

We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair-correlation function g(x)~x(-a). Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double ɛ=4-d, δ=4-a expansion.

Critical phenomena on scale-free networks: logarithmic corrections and scaling functions.

In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices, such corrections appear at some marginal values of the order parameter or space dimension. We present scaling relations for these exponents.

Coupled order-parameter system on a scale-free network.

The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value.

Field theory of bicritical and tetracritical points. III. Relaxational dynamics including conservation of magnetization (model C).

We calculate the relaxational dynamical critical behavior of systems of O(n_{ parallel}) plus sign in circleO(n_{ perpendicular}) symmetry including conservation of magnetization by renormalization group theory within the minimal subtraction scheme in two-loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point, strong dynamical scaling holds, with the asymptotic dynamical critical exponent z=2varphinu-1 , where varphi is the crossover exponent and nu the exponent of the correlation length. The critical dynamics at n_{ parallel}=1 and n_{ perpendicular}=2 is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior.

Field theory of bicritical and tetracritical points. II. Relaxational dynamics.

We calculate the relaxational dynamical critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by renormalization group method within the minimal subtraction scheme in two-loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds.

Field theory of bicritical and tetracritical points. I. Statics.

We calculate the static critical behavior of systems of O(n_||)(plus sign in circle)O(n_perpendicular) symmetry by the renormalization group method within the minimal subtraction scheme in two-loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability border lines in the space of the order parameter components n_|| and n_perpendicular and spatial dimension d are calculated.

Entropy-induced separation of star polymers in porous media.

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of f-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function g(r) approximately r-a.

Critical dynamics of diluted relaxational models coupled to a conserved density.

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a nonconserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics; however, it is the effective critical behavior that is often observed in experiments and in computer simulations, and this is described by the full set of dynamical equations of diluted model C. Indeed, different scenarios of effective critical behavior are predicted.

Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster.

The scaling properties of self-avoiding walks on a d -dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Phys. Rev.

Two-dimensional copolymers and multifractality: comparing perturbative expansions, Monte Carlo simulations, and exact results.

We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling dimensions derived by a conformal invariance technique in the context of D=2 quantum gravity. A simple Monte Carlo simulation brings about reasonable agreement with both approaches.