arXiv subjects

Ivan Dornic

Publications and source records attributed to Ivan Dornic.

11 recordsLinked to original sources

arXiv2026

Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlev\'e VI distribution

We determine the full persistence probability distribution for a non-Markovian stochastic process, motivated by first-passage questions arising in interacting spin systems and allied systems. We show that this distribution is governed by a distinguished Painlev\'e VI system arising from an exact Fredholm Pfaffian structure associated with the integrable sech kernel, $K_{\mathrm{sech}}=1/(2 \pi \cosh[(x-y)/2])$. The universal persistence exponent originally obtained by Derrida, Hakim and Pasquier is recovered as an asymptotic observable and acquires a natural geometric interpretation. In the stationary scaling regime, the persistence probability admits an exact Pfaffian decomposition into even and odd Fredholm determinants of the integrable \emph{sech} kernel. These determinants are controlled by a unique global solution of a second-order nonlinear ordinary differential equation, which is identified as a particular Painlev\'e VI equation. The corresponding Painlev\'e VI connection problem determines the persistence exponent as a limiting value at infinity. We further show that the Painlev\'e VI system governing persistence admits a direct geometric interpretation: the relevant solution coincides with the mean curvature of a one-parameter family of Bonnet surfaces immersed in $\mathbb R^3$. A folding transformation between such surfaces singles out the Painlev\'e VI equation with Manin coefficients $[0,0,0,0]$, which in particular governs the universal persistence distribution in the symmetric Ising case. In this framework, the persistence exponent is identified with the asymptotic mean curvature of the associated surface.

math-ph↗

arXiv2018

Universal Painlevé VI Probability Distribution in Pfaffian Persistence and Gaussian First-Passage Problems with a sech-Kernel

We recast the persistence probability for the spin located at the origin of a half-space arbitrarily $m$-magnetized Glauber-Ising chain as a Fredholm Pfaffian gap probability generating function with a sech-kernel. This is then spelled out as a tau-function for a certain Painlevé VI transcendent, the persistence exponent $θ(m)/2$ emerging as an asymptotic decay rate. Using a known yet remarkable correspondence that relates Painlevé equations to Bonnet surfaces, the persistence probability also acquires a geometric meaning in terms of the mean curvature of the latter, and even a topological one at the magnetization-symmetric point. Since the same sech-kernel with an underlying Pfaffian structure shows up in a variety of Gaussian first-passage problems, our Painlevé VI provides their universal first-passage probability distribution, in a manner exactly analogous to the famous Painlevé II Tracy-Widom laws. The tail behavior in the magnetization-symmetric case of our full scaling function allows to recover the exact persistence exponent $θ(0)/2=3/16$ for the $2d$-diffusing random field or for random real Kac's polynomials, a particular result found very recently by Poplavskyi and Schehr (Phys. Rev. Lett. {\bf 121}, 150601 (2018)). Our Painlevé VI tau-function characterization of the persistence probability also bears a correspondence with a $c=1$ conformal field theory, the monodromy parameters giving the dimensions of the associated primary fields. Thereby $θ(0)/2=3 β/2$, with $β=1/8$ the Onsager-Yang magnetization exponent for the critical $2d$ Ising model. This relates a nonequilibrium exponent to ordinary static critical behavior in one more space dimension, and suggests more generally that methods of boundary conformal field theory should be helpful for determining the critical properties of other unsolved nonequilibrium $1d$ processes.

cond-mat.stat-mech↗

arXiv2012

Finite scale singularity in the renormalization group flow of a reaction-diffusion system

We study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a new (conjugated) universality class.

cond-mat.stat-mech↗

arXiv2012

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a $\tanh$ function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope, at the same time the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as: retention of the pulse shape during the transmission of impulses in a long nonlinear cavity; giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

nlin.PS↗

arXiv2006

Sticky grains do not change the universality class of isotropic sandpiles

We revisit the sandpile model with ``sticky'' grains introduced by Mohanty and Dhar [Phys. Rev. Lett. {\bf 89}, 104303 (2002)] whose scaling properties were claimed to be in the universality class of directed percolation for both isotropic and directed models. Simulations in the so-called fixed-energy ensemble show that this conclusion is not valid for isotropic sandpiles and that this model shares the same critical properties of other stochastic sandpiles, such as the Manna model. %as expected from the existence of an extra %conservation-law, absent in directed percolation. These results are strengthened by the analysis of the Langevin equations proposed by the same authors to account for this problem which we show to converge, upon coarse-graining, to the well-established set of Langevin equations for the Manna class. Therefore, the presence of a conservation law keeps isotropic sandpiles, with or without stickiness, away from the directed percolation class.

cond-mat.stat-mech↗

arXiv2005

Integration of Langevin Equations with Multiplicative Noise and Viability of Field Theories for Absorbing Phase Transitions

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.

cond-mat.stat-mech↗

arXiv2005

Langevin description of critical phenomena with two symmetric absorbing states

On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical integration in physical dimensions. Our findings fully account for and clarify the intricate picture known so far from the aggregation of partial results obtained with microscopic models. We argue that the direct transition from disorder to one of two absorbing states is best described as a (generalized) voter critical point and show that it can be split into an Ising and a directed percolation transitions in dimensions larger than one.

cond-mat.stat-mech↗

arXiv2003

Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models

We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm the recent proposal that, at critical points, the large-time ``fluctuation-dissipation ratio'' $X_\infty$ is a universal amplitude ratio and find in particular $X_\infty \approx 0.33(2)$ and $X_\infty = 1/2$ for the magnetization in, respectively, the two-dimensional Ising and voter universality classes.

cond-mat.stat-mech↗

arXiv2001

Critical Coarsening without Surface Tension: the Voter Universality Class

We show that the two-dimensional voter model, usually considered to only be a marginal coarsening system, represents a broad class of models for which phase-ordering takes place without surface tension. We argue that voter-like growth is generically observed at order-disorder nonequilibrium transitions solely driven by interfacial noise between dynamically symmetric absorbing states.

cond-mat.stat-mech↗

arXiv2000

Analytical results for generalized persistence properties of smooth processes

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the diffusion equation evolving from random initial conditions, one of the simplest coarsening systems. Exact results are obtained in certain limits, and rely on a new method to deal with constrained multiplicative processes. An excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found.

cond-mat.stat-mech↗

arXiv1994

Mapping Self-Organized Criticality onto Criticality

We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical point. More precisely, SOC is shown to result from the tuning of the {\em order parameter} to a vanishingly small, but {\em positive} value, thus ensuring that the corresponding control parameter lies exactly at its critical value for the underlying transition. This clarifies the role and nature of the {\em very slow driving rate} common to all systems exhibiting SOC. This mechanism is shown to apply to models of sandpiles, earthquakes, depinning, fractal growth and forest-fires, which have been proposed as examples of SOC.

adap-org↗