arXiv subjects

R. Folk

Publications and source records attributed to R. Folk.

At least 19 recordsLinked to original sources

arXiv2024

Richard Kirwan a [united] Irish man of science in Europe

The late eighteenth and early nineteenth centuries have long been considered as a formative period for modern Irish political traditions such as nationalism, republicanism and unionism. For Europe it was the time of a turnover in science moving from observation to experiment and from speculation to fact. Richard Kirwan was a well known natural philosopher in Europe and a respected man of science in his time. Throughout all the wars, he was connected with his colleagues in a network reaching across Europe and even to America. Using a few examples, this article is intended to provide an insight how the network worked in a time that was marked by political conflicts and revolutionary events in both science and social life.

physics.hist-ph↗

arXiv2020

Crossing borders in the 19th century and now -- two examples of weaving a scientific network

Scientific research is and was at all times a transnational (global) activity. In this respect, it crosses several borders: national, cultural, and ideological. Even in times when physical borders separated the scientific community, scientists kept their minds open to the ideas created beyond the walls and tried to communicate despite all the obstacles. An example of such activities in the field of physics is the travel in the year 1838 of a group of three scientists through the Western Europe: Andreas Ettingshausen (professor at the University of Vienna), August Kunzek (professor at the University of Lviv) and P. Marian Koller (director of the observatory in Chremsminster, Upper Austria). 155 years later a vivid scientific exchange began between physicists from Austria and Ukraine, in particular, between the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine in Lviv and the Institute for Theoretical Physics of Johannes Kepler University Linz. This became possible due to the programs financed by national institutions, but it had its scientific background in already knotted historic scientific networks, when Lviv was an international center of mathematics and in Vienna the 'School of Statistical Thought' arose. Due to the new collaboration, after the breakup of the Soviet Union, Ukraine became the first country to join the Middle European Cooperation in Statistical Physics (MECO) founded in the early 1970s with the aim of bridging the gap between scientists from the Eastern and Western parts of Europe separated by the iron curtain.

physics.hist-ph↗

arXiv2017

Helmholtz decomposition theorem and Blumenthal's extension by regularization

Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for any asymptotically weakly decreasing vector field. He used a regularization method in his proof which can be extended to prove the theorem even for vector fields asymptotically increasing sublinearly. Blumenthal's result is then applied to the time-dependent fields of the dipole radiation and an artificial sublinearly increasing field.

physics.class-ph↗

arXiv2016

Phase diagram of Model C in the parametric space of order parameter and space dimensions

The scaling behavior of model C describing the dynamical behaviour of the $n$-component nonconserved order parameter coupled statically to a scalar conserved density is considered in $d$-dimensional space. Conditions for the realization of different types of scaling regimes in the $(n,d)$ plane are studied within the field-theoretical renormalization group approach. Borders separating these regions are calculated on the base of high-order RG functions using $ε$-expansions as well as by fixed dimension $d$ approach with resummation.

cond-mat.stat-mech↗

arXiv2015

The Helmholtz decomposition of decreasing and weakly increasing vector fields

Helmholtz decomposition theorem for vector fields is presented usually with too strong restrictions on the fields. Based on the work of Blumenthal of 1905 it is shown that the decomposition of vector fields is not only possible for asymptotically weakly decreasing vector fields, but even for vector fields, which asymptotically increase sublinearly. Use is made of a regularizatin of the Greens function and the mathematics of the proof is formulated as simply as possible. We also show a few examples for the decomposition of vector fields including the electric dipole radiation.

physics.class-ph↗

arXiv2012

Marginal dimensions for multicritical phase transitions

The field-theoretical model describing multicritical phenomena with two coupled order parameters with n_{||} and n_{\perp} components and of O(n_{||}) \oplus O(n_{\perp}) symmetry is considered. Conditions for realization of different types of multicritical behaviour are studied within the field-theoretical renormalization group approach. Surfaces separating stability regions for certain types of multicritical behaviour in parametric space of order parameter dimensions and space dimension d are calculated using the two-loop renormalization group functions. Series for the order parameter marginal dimensions that control the crossover between different universality classes are extracted up to the fourth order in \varepsilon=4-d and to the fifth order in a pseudo-\varepsilon parameter using the known high-order perturbative expansions for isotropic and cubic models. Special attention is paid to a particular case of O(1) \oplus O(2) symmetric model relevant for description of anisotropic antiferromagnets in an external magnetic field.

cond-mat.stat-mech↗

arXiv2011

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

This article concludes a series of papers (R. Folk, Yu. Holovatch, and G. 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. Here, we give the complete two loop calculation and analysis of the dynamic renormalization-group flow equations at the multicritical point in anisotropic antiferromagnets in an external magnetic field. We find that the time scales of the order parameters characterizing the parallel and perpendicular ordering with respect to the external field scale in the same way. This holds independent whether the Heisenberg fixed point or the biconical fixed point in statics is the stable one. The non-asymptotic analysis of the dynamic flow equations shows that due to cancelation effects the critical behavior is described - in distances from the critical point accessible to experiments - by the critical behavior qualitatively found in one loop order. Although one may conclude from the effective dynamic exponents (taking almost their one loop values) that weak scaling for the order parameter components is valid, the flow of the time scale ratios is quite different and they do not reach their asymptotic values.

cond-mat.stat-mech↗

arXiv2011

Entropic equation of state and scaling functions near the critical point in 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 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. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.

cond-mat.stat-mech↗

arXiv2010

Biconical critical dynamics

A complete two loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in anisotropic antiferromagnets in an external magnetic field is performed. Although strong scaling for the two order parameters (OPs) perpendicular and parallel to the field is restored as found earlier, in the experimentally accessible region the effective dynamical exponents for the relaxation of the OPs remain different since their equal asymptotic values are not reached.

cond-mat.stat-mech↗

arXiv2010

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 new scaling relations for these exponents. We also consider a spin system on a scale-free network which exhibits logarithmic corrections due to the specific network properties. To this end, we analyze the phase behavior of a model with coupled order parameters on a scale-free network and extract leading and logarithmic correction-to-scaling exponents that determine its field- and temperature behavior. Although both non-trivial sets of exponents emerge from the correlations in the network structure rather than from the spin fluctuations they fulfil the respective thermodynamic scaling relations. For the scale-free networks the logarithmic corrections appear at marginal values of the node degree distribution exponent. In addition we calculate scaling functions, which also exhibit nontrivial dependence on intrinsic network properties.

cond-mat.stat-mech↗

arXiv2009

Ground states of anisotropic antiferromagnets with single ion and cubic anisotropy

Anisotropic antiferromagnets in an external magnetic field show a rich variety of different ground states meeting in transition lines and multicritical points. We study the dependence of the ground states of these systems in the three dimensional space on physical parameters as exchange, single ion and cubic anisotropy. One identifies four different ground states: the paramagnetic (PM), the antiferromagnetic (AF), the spin flop (SF) and the biconical (BC) ground state. In the case of absence of a cubic anisotropy the transition lines separating the different ground states can be calculated analytically, otherwise they have to be calculated numerically. We also considered the behavior of the staggered magnetization which characterizes the different ground states. From its behavior the order of the transition from one state to the other is determined. But also the order of the transition changes along the transition lines when including the cubic anisotropy, especially at the reeentrant region where a transition from SF to BC and back to SF by increasing the external field $H$ occurs. Multicritical points are founded which are assumed to be tricritical or critical endpoints. The results obtained may be relevant for other systems since the antiferromagnetic model can be mapped to a lattice gas model where the biconical ground state is interpreted as supersolid phase. Recent renormalization group calculations show that such a phase would indicate the existence of a tetracritical point.

cond-mat.stat-mech↗

arXiv2009

Field Theoretical Approach to Bicritical and Tetracritical Behavior: Static and Dynamics

We discuss the static and dynamic multicritical behavior of three-dimensional systems of $O(n_\|)\oplus O(n_\perp)$ symmetry as it is explained by the field theoretical renormalization group method. Whereas the static renormalization group functions are currently know within high order expansions, we show that an account of two loop contributions refined by an appropriate resummation technique gives an accurate quantitative description of the multicritical behavior. One of the essential features of the static multicritical behavior obtained already in two loop order for the interesting case of an antiferromagnet in a magnetic field ($n_\|=1$, $n_\perp=2$) are the stability of the biconical fixed point and the neighborhood of the stability border lines to the other fixed points leading to very small transient exponents. We further pursue an analysis of dynamical multicritical behavior choosing different forms of critical dynamics and calculating asymptotic and effective dynamical exponents within the minimal subtraction scheme.

cond-mat.stat-mech↗

arXiv2009

Concentration and mass dependence of transport coefficients and correlation functions in binary mixtures with high mass-asymmetry

Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio $μ$, including the limiting case $μ=\infty$, for different mole fractions $x$. Within a large range of $x$ and $μ$ the product of the diffusion coefficient of the heavy species $D_{2}$ and the total shear viscosity of the mixture $η_{m}$ is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function and the van Hove correlation function.

cond-mat.soft↗

arXiv2009

A 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 non-zero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale free network there are notable differences for the amplitude ratios and susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T<T_c, when O(n) symmetry is present. This behavior is related to the appearance of Goldstone modes.

cond-mat.stat-mech↗

arXiv2008

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 $O(n_\|)\oplus O(n_\perp)$ symmetry including conservation of magnetization by renormalization group (RG) 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 $z=2ϕ/ν-1$ where $ϕ$ is the crossover exponent and $ν$ the exponent of the correlation length. The critical dynamics at $n_\|=1$ and $n_\perp=2$ is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen e.g. in the temperature dependence of the magnetic transport coefficients.

cond-mat.stat-mech↗

arXiv2008

Field theory of bi- and tetracritical points: Relaxational dynamics

We calculate the relaxational dynamical critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ 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. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point corresponding to the static biconical and the decoupled fixed point a very small dynamic transient exponent, of $ω_v^{\cal B}=0.0044$, is present in the dynamics for the physically important case $n_\|=1$ and $n_\perp=2$ in $d=3$.

cond-mat.stat-mech↗

arXiv2008

Field theory of bi- and tetracritical points: Statics

We calculate the static critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability boarder lines in the space of order parameter components $n_\|$ and $n_\perp$ and spatial dimension $d$ are calculated. The essential features obtained already in two loop order for the interesting case of an antiferromagnet in a magnetic field ($n_\|=1$, $n_\perp=2$) are the stability of the biconical fixed point and the neighborhood of the stability border lines to the other fixed points leading to very small transient exponents. We are also able to calculate the flow of static couplings, which allows to consider the attraction region. Depending on the nonuniversal background parameters the existence of different multicritical behavior (bicritical or tetracritical) is possible including a triple point.

cond-mat.stat-mech↗

arXiv2007

Model C critical dynamics of random anisotropy magnets

We study the relaxational critical dynamics of the three-dimensional random anisotropy magnets with the non-conserved n-component order parameter coupled to a conserved scalar density. In the random anisotropy magnets the structural disorder is present in a form of local quenched anisotropy axes of random orientation. When the anisotropy axes are randomly distributed along the edges of the n-dimensional hypercube, asymptotical dynamical critical properties coincide with those of the random-site Ising model. However structural disorder gives rise to considerable effects for non-asymptotic critical dynamics. We investigate this phenomenon by a field-theoretical renormalization group analysis in the two-loop order. We study critical slowing down and obtain quantitative estimates for the effective and asymptotic critical exponents of the order parameter and scalar density. The results predict complex scenarios for the effective critical exponent approaching an asymptotic regime.

cond-mat.dis-nn↗