arXiv subjects

Petter Minnhagen

Publications and source records attributed to Petter Minnhagen.

At least 55 records · Page 3Linked to original sources

arXiv2007

Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation

The origin of scale-free degree distributions in the context of networks is addressed through an analogous non-network model in which the node degree corresponds to the number of balls in a box and the rewiring of links to balls moving between the boxes. A statistical mechanical formulation is presented and the corresponding Hamiltonian is derived. The energy, the entropy, as well as the degree distribution and its fluctuations are investigated at various temperatures. The scale-free distribution is shown to correspond to the degenerate ground state, which has small fluctuations in the degree distribution and yet a large entropy. We suggest an implication of our results from the viewpoint of the stability in evolution of networks.

cond-mat.stat-mech↗

arXiv2006

CFT description of the Fully Frustrated XY model and phase diagram analysis

Following a suggestion given in Nucl. Phys. B 300 (1988)611,we show how the U(1)*Z_{2} symmetry of the fully frustrated XY (FFXY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at "paired states" fillings nu =1 (cfr. Cristofano et al.,Mod. Phys. Lett. A 15 (2000)1679;Nucl. Phys. B 641 (2002)547). The resulting twisted conformal field theory (CFT) with central charge c=2 is shown to well describe the physical properties of the FFXY model. In particular the whole phase diagram is recovered by analyzing the flow from the Z_{2} degenerate vacuum of the c=2 CFT to the infrared fixed point unique vacuum of the c=3/2 CFT. The last theory is known to successfully describe the critical behavior of the system at the overlap temperature for the Ising and vortex-unbinding transitions.

hep-th↗

arXiv2006

Models and average properties of scale-free directed networks

We extend the merging model for undirected networks by Kim et al. [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile merging, give rise to two distinct network types. We uncover that some non-trivial features of these two network types resemble two levels of a certain randomization/non-specificity in the link reshuffling during network evolution. Furthermore the same features show up, respectively, in metabolic networks and transcriptional networks. We introduce measures that single out the distinguishing features between the two prototype networks, as well as point out features which are beyond the prototypes.

cond-mat.stat-mech↗

arXiv2006

Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder

We numerically investigate dynamic critical behaviors of two-dimensional (2D) Josephson-junction arrays with positional disorder in the scheme of the resistively shunted junction dynamics. Large-scale computation of the current voltage characteristics reveals an evidence supporting that a phase transition occurs at a nonzero critical temperature in the strong disorder regime, as well as in the weak disorder regime. The phase transition at weak disorder appears to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast, evidence for a non-BKT transition is found in the strong disorder regime. These results are consistent with the recent experiment %by Yun {\it et al.} in cond-mat/0509151 on positionally disordered Josephson-junction arrays; in particular, the critical temperature of the non-BKT transition (ranging from 0.265 down to the minimum 0.22 in units of $E_J/k_B$ with the Josephson coupling strength $E_J$), the correlation length critical exponent $ν=1.2$, and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree with the existing studies of the 2D gauge-glass model.

cond-mat.supr-con↗

arXiv2004

Correlations in Networks associated to Preferential Growth

Combinations of random and preferential growth for both on-growing and stationary networks are studied and a hierarchical topology is observed. Thus for real world scale-free networks which do not exhibit hierarchical features preferential growth is probably not the main ingredient in the growth process. An example of such real world networks includes the protein-protein interaction network in yeast, which exhibits pronounced anti-hierarchical features.

cond-mat.dis-nn↗

arXiv2004

Self Organized Scale-Free Networks from Merging and Regeneration

We consider the self organizing process of merging and regeneration of vertices in complex networks and demonstrate that a scale-free degree distribution emerges in a steady state of such a dynamics. The merging of neighbor vertices in a network may be viewed as an optimization of efficiency by minimizing redundancy. It is also a mechanism to shorten the distance and thus decrease signaling times between vertices in a complex network. Thus the merging process will in particular be relevant for networks where these issues related to global signaling are of concern.

nlin.AO↗

arXiv2004

A simple model for self organization of bipartite networks

We suggest a minimalistic model for directed networks and suggest an application to injection and merging of magnetic field lines. We obtain a network of connected donor and acceptor vertices with degree distribution $1/s^2$, and with dynamical reconnection events of size $Δs$ occurring with frequency that scale as $1/Δs^3$. This suggest that the model is in the same universality class as the model for self organization in the solar atmosphere suggested by Hughes et al.(PRL {\bf 90} 131101).

nlin.AO↗

arXiv2004

Hierarchy Measures in Complex Networks

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with $γ$ -- the exponent of a degree distribution -- reaching its highest possible value for $γ\leq 2$ and quickly approaching zero for $γ>3$.

cond-mat.soft↗

arXiv2003

Scaling determination of the nonlinear I-V characteristics for 2D superconducting networks

It is shown from computer simulations that the current-voltage ($I$-$V$) characteristics for the two-dimensional XY model with resistively-shunted Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size scaling form from which the nonlinear $I$-$V$ exponent $a$ can be determined to good precision. This determination supports the conclusion $a=z+1$, where $z$ is the dynamic critical exponent. The results are discussed in the light of the contrary conclusion reached by Tang and Chen [Phys. Rev. B {\bf 67}, 024508 (2003)] and the possibility of a breakdown of scaling suggested by Bormann [Phys. Rev. Lett. {\bf 78}, 4324 (1997)].

cond-mat.supr-con↗

arXiv2003

Prisoners' dilemma in real-world acquaintance networks: Spikes and quasi-equilibria induced by the interplay between structure and dynamics

We study Nowak and May's spatial prisoners' dilemma game driven by mutations (random choices of suboptimal strategies) on empirical social networks. The time evolution of the cooperation level is highly complex containing spikes and steps between quasi-stable levels. A statistical characterization of the quasi-stable states and a study of the mechanisms behind the steps are given. We argue that the crucial structural ingredients causing the observed behavior is an inhomogeneous degree distribution and that the connections within vertices of highest degree are rather sparse. Based on these observations we construct model networks with a similarly complex time-evolution of the cooperation level.

cond-mat.dis-nn↗

arXiv2003

Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump

It is numerically shown that the discontinuous character of the helicity modulus of the two-dimensional XY model at the Kosterlitz-Thouless (KT) transition can be directly related to a higher order derivative of the free energy without presuming any {\it a priori} knowledge of the nature of the transition. It is also suggested that this higher order derivative is of intrinsic interest in that it gives an additional characteristics of the KT transition which might be associated with a universal number akin to the universal value of the helicity modulus at the critical temperature.

cond-mat.supr-con↗

arXiv2003

Dynamic critical behavior of the XY model in small-world networks

The critical behavior of the XY model on small-world network is investigated by means of dynamic Monte Carlo simulations. We use the short-time relaxation scheme, i.e., the critical behavior is studied from the nonequilibrium relaxation to equilibrium. Static and dynamic critical exponents are extracted through the use of the dynamic finite-size scaling analysis. It is concluded that the dynamic universality class at the transition is of the mean-field nature. We also confirm numerically that the value of dynamic critical exponent is independent of the rewiring probability P for P > 0.03.

cond-mat.dis-nn↗

arXiv2003

Phase Transitions in the Two-Dimensional Random Gauge XY Model

The two-dimensional random gauge \xy model, where the quenched random variables are magnetic bond angles uniformly distributed within $[-rπ, rπ]$ ($0 \leq r \leq 1$), is studied via Monte Carlo simulations. We investigate the phase diagram in the plane of the temperature $T$ and the disorder strength $r$, and infer, in contrast to a prevailing conclusion in many earlier studies, that the system is superconducting at any disorder strength $r$ for sufficiently low $T$. It is also argued that the superconducting to normal transition has different nature at weak disorder and strong disorder: termed Kosterlitz-Thouless (KT) type and non-KT type, respectively. The results are compared to earlier works.

cond-mat.supr-con↗

arXiv2002

Comment on ``Loss of Superconducting Phase Coherence in YBa_2Cu_3O_7 Films: Vortex-Loop Unbinding and Kosterlitz-Thouless Phenomena''

Recently, Kotzler et al. measured the frequency-dependent conductance for YBa_2Cu_3O_7 and interpreted their results as evidences that the decay of the superfluid density is caused by a 3D vortex loop proliferation mechanism and a dimensional crossover when the correlation length $ξ_c$ along the c axis becomes comparable to the sample thickness $d$ [PRL 87, 127005(2001)]. In this Comment, we show that the complex conductance data presented by Kotzler et al. have characteristic key features not compatible with their analysis, which are instead described by the existing phenomenology of 2D vortex fluctuation associated with a partial decoupling of CuO_2-planes.

cond-mat.supr-con↗

arXiv2002

Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.

cond-mat.dis-nn↗

arXiv2002

Dynamic transitions and resonances in Josephson-junction arrays under oscillating magnetic fields

We investigate dynamic transitions and stochastic resonance phenomena in two-dimensional fully frustrated Josephson-junction arrays driven by staggered oscillating magnetic fields. As the temperature is lowered, the dynamic order parameter, defined to be the average staggered magnetization, is observed to acquire nonzero values. The resulting transition is found to belong to the same universality as the equilibrium Z_2 transition for small driving amplitudes while large driving fields appear to induce deviation from the universality class. The transition is also manifested by the stochastic resonance peak of the signal-to-noise ratio, which develops above the transition temperature.

cond-mat↗

arXiv2002

Splitting of the superconducting transition in the two weakly coupled 2D XY models

The frequency $ω$ and temperature T dependent complex conductivity $σ$ of two weakly coupled 2D XY models subject to the RSJ dynamics is studied through computer simulations. A double dissipation-peak structure in $Re[ωσ]$ is found as a function of T for a fixed frequency. The characteristics of this double-peak structure, as well as its frequency dependence, is investigated with respect to the difference in the critical temperatures of the two XY models, originating from their different coupling strengths. The similarity with the experimental data in Festin {\it et al.} [Physica C 369, 295 (2002)] for a thin YBCO film is pointed out and some possible implications are suggested.

cond-mat.supr-con↗

arXiv2001

XY model in small-world networks

The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte-Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally-coupled XY model.

cond-mat.stat-mech↗