arXiv subjects

R. Folk

Publications and source records attributed to R. Folk.

45 records · Page 3Linked to original sources

arXiv2000

Pseudo--epsilon expansion of six--loop renormalization group functions of an anisotropic cubic model

Six-loop massive scheme renormalization group functions of a d=3-dimensional cubic model (J.M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B vol. 61, 15136 (2000)) are reconsidered by means of the pseudo-epsilon expansion. The marginal order parameter components number N_c=2.862(5) as well as critical exponents of the cubic model are obtained. Our estimate N_c<3 leads in particular to the conclusion that all ferromagnetic cubic crystals with three easy axis should undergo a first order phase transition.

cond-mat.stat-mech↗

arXiv2000

Molecular dynamics simulations of spin and pure liquids with preserving all the conservation laws

A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the time step, all the conservation laws inherent in the description without breaking the time reversibility. As a result, an implicit second-order algorithm is derived and applied to pure as well as spin liquids for which the dynamics is characterized by the conservation of total energy, linear and angular momenta as well as magnetization and individual spin lengths. It is demonstrated on the basis of Lennard-Jones and Heisenberg fluid models that when such quantities as energy and magnetization must be conserved perfectly, the new algorithm turns out to be more efficient than popular decomposition integrators and standard predictor-corrector schemes.

cond-mat.stat-mech↗

arXiv2000

Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling (FSS) technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent $α$. The appearance of such new corrections to scaling is a general feature of systems with constraints.

cond-mat.stat-mech↗

arXiv2000

Conservation-laws-preserving algorithms for spin dynamics simulations

We propose new algorithms for numerical integration of the equations of motion for classical spin systems with fixed spatial site positions. The algorithms are derived on the basis of a mid-point scheme in conjunction with the multiple time staging propagation. Contrary to existing predictor-corrector and decomposition approaches, the algorithms introduced preserve all the integrals of motion inherent in the basic equations. As is demonstrated for a lattice ferromagnet model, the present approach appears to be more efficient even over the recently developed decomposition method.

cond-mat.stat-mech↗

arXiv2000

Algorithm for molecular dynamics simulations of spin liquids

A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the algorithm exactly conserves spin lengths and can be used with much larger time steps than those inherent in standard predictor-corrector schemes. The results obtained for time correlation functions demonstrate the evident dynamic interplay between the liquid and magnetic subsystems.

cond-mat.soft↗

arXiv2000

Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus $ε^{1/2}$-Expansion

We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $ϕ^4$-theory with O(n)-symmetric and cubic interactions (H.Kleinert and V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction scheme allows to develop either the $ε^{1/2}$-expansion series or to proceed in the 3d approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents providing a local measure for the degree of singularity of different physical quantities in the critical region. We report resummed numerical values for the effective and asymptotic critical exponents. Obtained within the 3d approach results agree pretty well with recent Monte Carlo simulations. $ε^{1/2}$-expansion does not allow reliable estimates for d=3.

cond-mat↗

arXiv2000

Critical light scattering in liquids

We compare theoretical results for the characteristic frequency of the Rayleigh peak calculated in one-loop order within the field theoretical method of the renormalization group theory with experiments and other theoretical results. Our expressions describe the non-asymptotic crossover in temperature, density and wave vector. In addition we discuss the frequency dependent shear viscosity evaluated within the same model and compare our theoretical results with recent experiments in microgravity.

cond-mat↗

arXiv1998

The correction-to-scaling exponent in dilute systems

The leading correction-to-scaling exponent $ω$ for the three-dimensional dilute Ising model is calculated in the framework of the field theoretic renormalization group approach. Both in the minimal subtraction scheme as well as in the massive field theory (resummed four loop expansion) excellent agreement with recent Monte Carlo calculations [Ballesteros H G, et al Phys. Rev. B 58, 2740 (1998)] is achieved. The expression of $ω$ as series in a $\sqrtε$-expansion up to ${\cal O}(ε^2)$ does not allow a reliable estimate for $d=3$.

cond-mat↗

arXiv1998

Critical fluctuations in normal-to-superconducting transition

We study the phase transition to the superconducting state taking into account the fluctuations of the order parameter and of the vector magnetic field and discuss the question of the order of transition occuring in this model. We use the field-theoretical renormalization group approach and consider in two-loop approximation the gauge model for a superconductor, generalized to a n/2 component complex order parameter. Special attention is being payed to the fact, that the corresponding series might be asymptotic ones and therefore have zero radius of convergence. We review different ways of analytical continuation of the series and applying Pade analysis and Pade-Borel resummation technique conclude that in the model under consideration still exists a possibility for the second-order phase transition with the critical exponents differing from those of a superfluid liquid.

cond-mat↗