Biomedical subjects

Ferenc Iglói

Publications and source records attributed to Ferenc Iglói.

8 recordsLinked to original sources

PubMed2006

Nonequilibrium phase transitions and finite-size scaling in weighted scale-free networks.

We consider nonequilibrium phase transitions, such as epidemic spreading, in weighted scale-free networks, in which highly connected nodes have a relatively smaller ability to transfer infection. We solve the dynamical mean-field equations and discuss finite-size scaling theory. The theoretical predictions are confronted with the results of large scale Monte Carlo simulations on the weighted Barabási-Albert network. Local scaling exponents are found different at a typical site and at a node with very large connectivity.

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PubMed2005

Partially asymmetric zero-range process with quenched disorder.

We consider the one-dimensional partially asymmetric zero-range process where the hopping rates as well as the easy direction of hopping are random variables. For this type of disorder there is a condensation phenomenon in the thermodynamic limit: the particles typically occupy one single site and the fraction of particles outside the condensate is vanishing. We use extreme value statistics and an asymptotically exact strong disorder renormalization group method to explore the properties of the steady state. In a finite system of L sites the current vanishes as J approximately L(-z), where the dynamical exponent, z, is exactly calculated. For 0 < z < 1 the transport is realized by N(a) approximately L(1-z) active particles, which move with a constant velocity, whereas for z > 1 the transport is due to the anomalous diffusion of a single Brownian particle. Inactive particles are localized at a second special site and their number in rare realizations is macroscopic. The average density profile of inactive particles has a width of xi approximately delta(-2) in terms of the asymmetry parameter delta. In addition to this, we have investigated the approach to the steady state of the system through a coarsening process and found that the size of the condensate grows as n(L) approximately t(1/(1+z)) for large times. For the unbiased model z is formally infinite and the coarsening is logarithmically slow.

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PubMed2005

Partially asymmetric exclusion models with quenched disorder.

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case, the accumulated distance traveled by the particles, x, scales with the time, t, as x approximately t(1/z), with a dynamical exponent z>0. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method, we exactly calculate z(PW) for particlewise disorder, which is argued to be related as z(SW)=z(PW)/2 for sitewise disorder. In the symmetric case with zero mean drift, the particle diffusion is ultraslow, logarithmic in time.

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PubMed2004

Absorbing state phase transitions with quenched disorder.

Quenched disorder--in the sense of the Harris criterion--is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for a weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.

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PubMed2004

Nonequilibrium critical dynamics at surfaces: cluster dissolution and nonalgebraic correlations.

We study nonequilibrium dynamical properties at a free surface after the system is quenched from the high-temperature phase into the critical point. We show that if the spatial surface correlations decay sufficiently rapidly the surface magnetization and/or the surface manifold autocorrelations have a qualitatively different universal short time behavior than the same quantities in the bulk. At a free surface cluster dissolution may take place instead of domain growth, yielding stationary dynamical correlations that decay in a stretched exponential form. This phenomenon takes place in the three-dimensional Ising model and should be observable in real ferromagnets.

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PubMed2003

Strong disorder fixed point in absorbing-state phase transitions.

The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: beta=(3-sqrt[5])/2 and nu( perpendicular )=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.

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PubMed2002

Percolation in a random environment.

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are nonuniversal, whereas for strong enough disorder the system scales into an infinite randomness fixed point in which the critical exponents are exactly known.

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PubMed2002

First- and second-order phase transitions in scale-free networks.

We study first- and second-order phase transitions of ferromagnetic lattice models on scale-free networks, with a degree exponent gamma. Using the example of the q-state Potts model we derive a general self-consistency relation within the frame of the Weiss molecular-field approximation, which presumably leads to exact critical singularities. Depending on the value of gamma, we have found three different regimes of the phase diagram. As a general trend first-order transitions soften with decreasing gamma and the critical singularities at the second-order transitions are gamma dependent.

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