arXiv subjects

Ferenc Iglói

Publications and source records attributed to Ferenc Iglói.

53 records · Page 3Linked to original sources

arXiv2007

Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain

We study the distribution of finite size pseudo-critical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudo-critical points are defined in three different ways: the position of the maximum of the average entanglement entropy, the scaling behavior of the surface magnetization, and the energy of a soft mode. All three lead to a log-normal distribution of the pseudo-critical transverse fields, where the width scales as $L^{-1/ν}$ with $ν=2$ and the shift of the average value scales as $L^{-1/ν_{typ}}$ with $ν_{typ}=1$, which we related to the scaling of average and typical quantities in the critical region.

cond-mat.dis-nn↗

arXiv2006

Geometrical clusters in two-dimensional random-field Ising models

We consider geometrical clusters (i.e. domains of parallel spins) in the square lattice random field Ising model by varying the strength of the Gaussian random field, $Δ$. In agreement with the conclusion of previous investigation (Phys. Rev. E{\bf 63}, 066109 (2001)), the geometrical correlation length, i.e. the average size of the clusters, $ξ$, is finite for $Δ> Δ_c \approx 1.65$ and divergent for $Δ\le Δ_c$. The scaling function of the distribution of the mass of the clusters as well as the geometrical correlation function are found to involve the scaling exponents of critical percolation. On the other hand the divergence of the correlation length, $ξ(Δ) \sim (Δ- Δ_c)^{-ν}$, with $ν\approx 2.$ is related to that of tricritical percolation. It is verified numerically that critical geometrical correlations transform conformally.

cond-mat.stat-mech↗

arXiv2006

Partially Asymmetric Exclusion Processes with Sitewise Disorder

We study the stationary properties as well as the non-stationary dynamics of the one-dimensional partially asymmetric exclusion process with position dependent random hop rates. In a finite system of $L$ sites the stationary current, $J$, is determined by the largest barrier and the corresponding waiting time, $τ\sim J^{-1}$, is related to the waiting time of a single random walker, $τ_{rw}$, as $τ\sim τ_{rw}^{1/2}$. The current is found to vanish as: $J \sim L^{-z/2}$, where $z$ is the dynamical exponent of the biased single particle Sinai walk. Typical stationary states are phase separated: At the largest barrier almost all particles queue at one side and almost all holes are at the other side. The high-density (low-density) region, is divided into $\sim L^{1/2}$ connected parts of particles (holes) which are separated by islands of holes (particles) located at the subleading barriers (valleys). We also study non-stationary processes of the system, like coarsening and invasion. Finally we discuss some related models, where particles of larger size or multiple occupation of lattice sites is considered.

cond-mat.stat-mech↗

arXiv2005

Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain

We use extensive density matrix renormalization group (DMRG) calculations to explore the phase diagram of the random S=1 antiferromagnetic Heisenberg chain with a power-law distribution of the exchange couplings. We use open chains and monitor the lowest gaps, the end-to-end correlation function, and the string order parameter. For this distribution at weak disorder, the systems is in the gapless Haldane phase with a disorder dependent dynamical exponent, z, and z=1 signals, the border between the nonsingular and singular regions of the local susceptibility. For strong enough disorder, which approximately corresponds to a uniform distribution, a transition into the random singlet phase is detected, at which the string order parameter as well as the average end-to-end correlation function are vanishing and at the same time the dynamical exponent is divergent. Singularities of physical quantities are found to be somewhat different in the random singlet phase and in the critical point.

cond-mat.stat-mech↗

arXiv2005

The 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 phenomena 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 $J \sim L^{-z}$, where the dynamical exponent, $z$, is exactly calculated. For $0 1$ 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, $ξ\sim δ^{-2}$, in terms of the asymmetry parameter, $δ$. 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 $n_L \sim t^{1/(1+z)}$ for large times. For the unbiased model $z$ is formally infinite and the coarsening is logarithmically slow.

cond-mat.stat-mech↗

arXiv2005

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

We consider nonequilibrium phase transitions in weighted scale-free networks, in which highly connected nodes, which are created earlier in time are partially immunized. For epidemic spreading 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.

cond-mat.stat-mech↗

arXiv2004

Disorder Induced Phases in Higher Spin Antiferromagnetic Heisenberg Chains

Extensive DMRG calculations for spin S=1/2 and S=3/2 disordered antiferromagnetic Heisenberg chains show a rather distinct behavior in the two cases. While at sufficiently strong disorder both systems are in a random singlet phase, we show that weak disorder is an irrelevant perturbation for the S=3/2 chain, contrary to what expected from a naive application of the Harris criterion. The observed irrelevance is attributed to the presence of a new correlation length due to enhanced end-to-end correlations. This phenomenon is expected to occur for all half-integer S > 1/2 chains. A possible phase diagram of the chain for generic S is also discussed.

cond-mat.stat-mech↗

arXiv2004

Antiferromagnetic Heisenberg chains with bond alternation and quenched disorder

We consider S=1/2 antiferromagnetic Heisenberg chains with alternating bonds and quenched disorder, which represents a theoretical model of the compound CuCl_{2x}Br_{2(1-x)}(γ-{pic})_2. Using a numerical implementation of the strong disorder renormalization group method we study the low-energy properties of the system as a function of the concentration, x, and the type of correlations in the disorder. For perfect correlation of disorder the system is in the random dimer (Griffiths) phase having a concentration dependent dynamical exponent. For weak or vanishing disorder correlations the system is in the random singlet phase, in which the dynamical exponent is formally infinity. We discuss consequences of our results for the experimentally measured low-temperature susceptibility of CuCl_{2x}Br_{2(1-x)}(γ-{pic})_2.

cond-mat.dis-nn↗

arXiv2002

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 $γ$. 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 $γ$, we have found three different regimes of the phase diagram. As a general trend first-order transitions soften with decreasing $γ$ and the critical singularities at the second-order transitions are $γ$-dependent.

cond-mat.stat-mech↗

arXiv2002

Percolation in 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 non-universal, whereas for strong enough disorder the system scales into an {\it infinite randomness fixed point} in which the critical exponents are exactly known.

cond-mat.stat-mech↗

arXiv2001

Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases

The real-space renormalization group (RG) treatment of random transverse-field Ising spin chains by Fisher ({\it Phys. Rev. B{\bf 51}, 6411 (1995)}) has been extended into the strongly ordered and strongly disordered Griffiths phases and asymptotically exact results are obtained. In the non-critical region the asymmetry of the renormalization of the couplings and the transverse fields is related to a non-linear quantum control parameter, $Δ$, which is a natural measure of the distance from the quantum critical point. $Δ$, which is found to stay invariant along the RG trajectories and has been expressed by the initial disorder distributions, stands in the singularity exponents of different physical quantities (magnetization, susceptibility, specific heat, etc), which are exactly calculated. In this way we have observed a weak-universality scenario: the Griffiths-McCoy singularities does not depend on the form of the disorder, provided the non-linear quantum control parameter has the same value. The exact scaling function of the magnetization with a small applied magnetic field is calculated and the critical point magnetization singularity is determined in a simple, direct way.

cond-mat.dis-nn↗

arXiv2001

Disorder induced cross-over effects at quantum critical points

Critical properties of quantum spin chains with varying degrees of disorder are studied at zero temperature by analytical and extensive density matrix renormalization methods. Generally the phase diagram is found to contain three phases. The weak disorder regime, where the critical behavior is controlled by the fixed points of the pure system and the strong disorder regime, which is attracted by an infinite randomness fixed point, are separated by an intermediate disorder regime, where dynamical scaling is anisotropic and the static and dynamical exponents are disorder dependent.

cond-mat.dis-nn↗

arXiv1999

Boundary critical behaviour of two-dimensional random Potts models

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the bulk and at the boundary. Using Monte Carlo techniques the surface and the bulk magnetizations are studied close to the critical temperature and the critical exponents $β_1$ and $β$ are determined. In the strip-like geometry the critical magnetization profile is investigated with free-fixed spin boundary condition and the characteristic scaling dimension, $β_1/ν$, is calculated from conformal field theory. The critical exponents and scaling dimensions are found monotonously increasing with q. Anomalous dimensions of the relevant scaling fields are estimated and the multifractal behaviour at criticality is also analyzed.

cond-mat.stat-mech↗

arXiv1999

Transverse-field Ising spin chain with inhomogeneous disorder

We consider the critical and off-critical properties at the boundary of the random transverse-field Ising spin chain when the distribution of the couplings and/or transverse fields, at a distance $l$ from the surface, deviates from its uniform bulk value by terms of order $l^{-κ}$ with an amplitude $A$. Exact results are obtained using a correspondence between the surface magnetization of the model and the surviving probability of a random walk with time-dependent absorbing boundary conditions. For slow enough decay, $κ<1/2$, the inhomogeneity is relevant: Either the surface stays ordered at the bulk critical point or the average surface magnetization displays an essential singularity, depending on the sign of $A$. In the marginal situation, $κ=1/2$, the average surface magnetization decays as a power law with a continuously varying, $A$-dependent, critical exponent which is obtained analytically. The behavior of the critical and off-critical autocorrelation functions as well as the scaling form of the probability distributions for the surface magnetization and the first gaps are determined through a phenomenological scaling theory. In the Griffiths phase, the properties of the Griffiths-McCoy singularities are not affected by the inhomogeneity. The various results are checked using numerical methods based on a mapping to free fermions.

cond-mat.stat-mech↗

arXiv1998

The McCoy-Wu Model in the Mean-field Approximation

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents $β\approx 3.6$ and $β_1 \approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $α\approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c) \sim t_c^ω$ and we show that the difference between the values of the critical exponents in the pure and in the random system is just $ω\approx 3.1$. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.

cond-mat.stat-mech↗

arXiv1995

Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation

We consider concentric circular defects in the two-dimensional Ising model, which are distributed according to a generalized Fredholm sequence, i. e. at exponentially increasing radii. This type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation. The critical exponent of the local magnetization is obtained through finite-size scaling, using a corner transfer matrix approach in the extreme anisotropic limit. It varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial Hilhorst-van Leeuwen model. Through a conformal mapping of the system onto a strip, the gap-exponent relation is shown to remain valid for such an aperiodic defect.

cond-mat↗

arXiv1995

Realization of supersymmetric quantum mechanics in inhomogeneous Ising models

Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In the present paper, this method is used in statistical physics. We consider the local critical behaviour of inhomogeneous Ising models and determine the complete set of anomalous dimensions from the spectrum of the corresponding transfer matrix in the strip geometry. For smoothly varying perturbations, the eigenvalue problem of the transfer matrix indeed takes the form of a Schrödinger equation, and the corresponding potential furthermore exhibits the shape invariance property for some known extended defects. In these cases, the complete spectrum is derived by the methods of supersymmetric quantum mechanics.

cond-mat↗