arXiv subjects

Michel Pleimling

Publications and source records attributed to Michel Pleimling.

At least 91 records · Page 5Linked to original sources

arXiv2008

Aging processes in reversible reaction-diffusion systems

Reversible reaction-diffusion systems display anomalous dynamics characterized by a power-law relaxation toward stationarity. In this paper we study in the aging regime the nonequilibrium dynamical properties of some model systems with reversible reactions. Starting from the exact Langevin equations describing these models, we derive expressions for two-time correlation and autoresponse functions and obtain a simple aging behavior for these quantities. The autoresponse function is thereby found to depend on the specific nature of the chosen perturbation of the system.

cond-mat.stat-mech↗

arXiv2007

Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.

cond-mat.stat-mech↗

arXiv2007

Phase-ordering kinetics of two-dimensional disordered Ising models

The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform disorder is investigated by intensive Monte Carlo simulations. Taking into account finite-time corrections to scaling, simple ageing behaviour is observed in the two-time responses and correlators. The dynamical exponent z and the form of the scaling functions only depend on the ratio eps/T, where eps describes the width of the distribution of the disorder. The agreement of the predictions of local scale-invariance generalised to z<> 2 for the two-time scaling functions of response and correlations with the numerical data provides a direct test of generalised Galilei-invariance.

cond-mat.stat-mech↗

arXiv2007

Local aging phenomena close to magnetic surfaces

Surface aging phenomena are discussed for semi-infinite systems prepared in a fully disordered initial state and then quenched to or below the critical point. Besides solving exactly the semi-infinite Ising model in the limit of large dimensions, we also present results of an extensive numerical study of the nonequilibrium dynamical behavior of the two-dimensional semi-infinite Ising model undergoing coarsening. The studied models reveal a simple aging behavior where some of the nonequilibrium surface exponents take on values that differ from their bulk counterparts. For the two-dimensional semi-infinite Ising model we find that the exponent $b_1$, that describes the scaling behavior of the surface autocorrelation, vanishes. These simulations also reveal the existence of strong finite-time corrections that to some extent mask the leading scaling behavior of the studied two-time quantities.

cond-mat.stat-mech↗

arXiv2007

Nonequilibrium critical relaxation at a first-order phase transition point

We study numerically the nonequilibrium dynamical behavior of an Ising model with mixed two-spin and four-spin interactions after a sudden quench from the high-temperature phase to the first-order phase transition point. The autocorrelation function is shown to approach its limiting value, given by the magnetization in the ordered phase at the transition point, m_c, through a stretched exponential decay. On the other hand relaxation of the magnetization starting with an uncorrelated initial state with magnetization, m_i, approaches either m_c, for m_i>0.5, or zero, for m_i<0.5. For small m_i and for m_i slightly larger than 0.5 the relaxation of the magnetization shows an asymptotic power-law time dependence, thus from a nonequilibrium point of view the transition is continuous.

cond-mat.stat-mech↗

arXiv2007

Local scale-invariance in disordered systems

Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can describe data for either non-glassy systems quenched to below $T_c$ or else for spin glasses at criticality. The dependence of the scaling behaviour on the distribution of the random couplings is discussed. It is shown that finite-time corrections to scaling can become quite sizable in these systems. Numerically determined ageing quantities are confronted with available experimental results.

cond-mat.stat-mech↗

arXiv2006

Symmetry based determination of space-time functions in nonequilibrium growth processes

We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and in 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.

cond-mat.stat-mech↗

arXiv2006

Ageing in disordered magnets and local scale-invariance

The ageing of the bond-disordered two-dimensional Ising model quenched to below its critical point is studied through the two-time autocorrelator and thermoremanent magnetization (TRM). The corresponding ageing exponents are determined. The form of the scaling function of the TRM is well described by the theory of local scale-invariance.

cond-mat.stat-mech↗

arXiv2006

On the identification of quasiprimary scaling operators in local scale-invariance

The relationship between physical observables defined in lattice models and the associated (quasi-)primary scaling operators of the underlying field-theory is revisited. In the context of local scale-invariance, we argue that this relationship is only defined up to a time-dependent amplitude and derive the corresponding generalizations of predictions for two-time response and correlation functions. Applications to non-equilibrium critical dynamics of several systems, with a fully disordered initial state and vanishing initial magnetization, including the Glauber-Ising model, the Frederikson-Andersen model and the Ising spin glass are discussed. The critical contact process and the parity-conserving non-equilibrium kinetic Ising model are also considered.

cond-mat.stat-mech↗

arXiv2006

Continuous phase transitions with a convex dip in the microcanonical entropy

The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as for example in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.

cond-mat.stat-mech↗

arXiv2005

Dynamic critical behaviour in Ising spin glasses

The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent $z_{\rm c}$, the non-equilibrium autocorrelation decay exponent $λ_c/z_{\rm c}$, and the critical fluctuation-dissipation ratio $X_{\infty}$ all vary strongly and systematically with the form of the interaction distribution.

cond-mat.dis-nn↗

arXiv2005

Reentrance during nonequilibrium relaxation

We consider nonequilibrium critical dynamics of the two-dimensional Ising model for which the initial state is prepared by switching on random fields with zero mean and variance $H$. In the initial state there is no magnetic order but the clusters of parallel spins have a percolation transition for small enough $H$. Using heath-bath dynamics we measure the relaxation of the magnetization which shows a reentrance in time. Due to cluster dissolution in the early time regime there is a decrease of the magnetization, followed by an increase due to nonequilibrium domain growth which itself turns to a decrease due to equilibrium relaxation. The power law decay of the nonequilibrium autocorrelation function is not influenced by the percolation in the initial state.

cond-mat.stat-mech↗

arXiv2005

Out-of-equilibrium properties of the semi-infinite kinetic spherical model

We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase, both for Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation ratio and the scaling functions of two-time surface correlation and response functions are determined explicitly in the dynamical scaling regime. In the low-temperature phase our results show that for the case of Dirichlet boundary conditions the value of the non-equilibrium surface exponent $b_1$ differs from the usual bulk value of systems undergoing phase ordering.

cond-mat.stat-mech↗

arXiv2005

Ageing without detailed balance in the bosonic contact and pair-contact processes: exact results

Ageing in systems without detailed balance is studied in the exactly solvable bosonic contact process and the critical bosonic pair-contact process. The two-time correlation function and the two-time response function are explicitly found. In the ageing regime, the dynamical scaling of these is analyzed and exact results for the ageing exponents and the scaling functions are derived. For the critical bosonic pair-contact process the autocorrelation and autoresponse exponents agree but the ageing exponents $a$ and $b$ are shown to be distinct.

cond-mat.stat-mech↗

arXiv2005

Reply to "Comment on 'Scaling of the linear response in simple ageing systems without disorder' "

The value of the non-equilibrium exponent $a$ is measured in the two-dimensional (2D) Ising model quenched to below criticality from the dynamical scaling of the zero-field-cooled and the intermediate susceptibility. Our results fully reconfirm the expected value $a=1/2$ but are inconsistent with the value $a=1/4$, advocated by Corberi, Lippiello and Zannetti (cond-mat/0506139).

cond-mat.stat-mech↗

arXiv2005

On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance

The frequency-dependent scaling of the dispersive and dissipative parts of the alternating susceptibility is studied for spin glasses at criticality. An extension of the usual $ωt$-scaling is proposed. Simulational data from the three-dimensional Ising spin glass agree with this new scaling form and moreover reproduce well the scaling functions explicitly calculated for systems satisfying local scale-invariance. There is also a qualitative agreement with existing experimental data.

cond-mat.stat-mech↗

arXiv2005

Microcanonical analysis of small systems

The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from the entropy. Response functions such as the susceptibility are for example related to the curvature of the entropy surface. Interestingly, physical quantities in the microcanonical ensemble show characteristic properties of phase transitions already in finite systems. In this paper we investigate these characteristics for finite Ising systems. The singularities in microcanonical quantities which announce a continuous phase transition in the infinite system are characterised by classical critical exponents. Estimates of the non-classical exponents which emerge only in the thermodynamic limit can nevertheless be obtained by analyzing effective exponents or by applying a microcanonical finite-size scaling theory. This is explicitly demonstrated for two- and three-dimensional Ising systems.

cond-mat.stat-mech↗

arXiv2005

The density of states of classical spin systems with continuous degrees of freedom

In the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions. In this approach the quantities of interest are exclusively expressed as derivatives of the entropy $S = \ln Ω$ where $Ω$ is the density of states. Obviously, the density of states has to be known with very high accuracy for this kind of analysis. Important progress has been achieved recently in the computation of the density of states of classical systems, as new types of algorithms have been developed. Here we extend one of these methods, originally formulated for systems with discrete degrees of freedom, to systems with continuous degrees of freedoms. As an application we compute the density of states of the three-dimensional XY model and demonstrate that critical quantities can directly be determined from the density of states of finite systems in cases where the degrees of freedom take continuous values.

cond-mat.stat-mech↗