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Malte Henkel

Publications and source records attributed to Malte Henkel.

At least 109 records · Page 6Linked to original sources
arXiv2004

Ageing in the critical contact process: a Monte Carlo study

The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations in one and two dimensions and through mean-field theory that time-translation invariance is broken and that dynamical scaling holds. We find that the autocorrelation and autoresponse exponents lambda_{Gamma} and lambda_R are equal but, in contrast to systems relaxing to equilibrium, the ageing exponents a and b are distinct. A recent proposal to define a non-equilibrium temperature through the short-time limit of the fluctuation-dissipation ratio is therefore not applicable.

cond-mat.stat-mech↗
arXiv2004

On nonlinear partial differential equations with an infinite-dimensional conditional symmetry

The invariance of nonlinear partial differential equations under a certain infinite-dimensional Lie algebra A_N(z) in N spatial dimensions is studied. The special case A_1(2) was introduced in J. Stat. Phys. {\bf 75}, 1023 (1994) and contains the Schrödinger Lie algebra sch_1 as a Lie subalgebra. It is shown that there is no second-order equation which is invariant under the massless realizations of A_N(z). However, a large class of strongly non-linear partial differential equations is found which are conditionally invariant with respect to the massless realization of A_N(z) such that the well-known Monge-Ampere equation is the required additional condition. New exact solutions are found for some representatives of this class.

math-ph↗
arXiv2004

Two-time autocorrelation function in phase-ordering kinetics from local scale-invariance

The time-dependent scaling of the two-time autocorrelation function of spin systems without disorder undergoing phase-ordering kinetics is considered. Its form is shown to be determined by an extension of dynamical scaling to a local scale-invariance which turns out to be a new version of conformal invariance. The predicted autocorrelator is in agreement with Monte-Carlo data on the autocorrelation function of the 2D kinetic Ising model with Glauber dynamics quenched to a temperature below criticality.

cond-mat.stat-mech↗
arXiv2004

Ageing phenomena without detailed balance: the contact process

The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is characterised through the dynamical scaling of the two-times autocorrelation and autoresponse functions. The observed non-equality of the ageing exponents a and b excludes the possibility of a finite fluctuation-dissipation ratio in the ageing regime. The scaling form of the critical autoresponse function is in agreement with the prediction of local scale-invariance.

cond-mat.stat-mech↗
arXiv2004

The non-equilibrium phase transition of the pair-contact process with diffusion

The pair-contact process 2A->3A, 2A->0 with diffusion of individual particles is a simple branching-annihilation processes which exhibits a phase transition from an active into an absorbing phase with an unusual type of critical behaviour which had not been seen before. Although the model has attracted considerable interest during the past few years it is not yet clear how its critical behaviour can be characterized and to what extent the diffusive pair-contact process represents an independent universality class. Recent research is reviewed and some standing open questions are outlined.

cond-mat.stat-mech↗
arXiv2004

Local scale-invariance and ageing in noisy systems

The influence of the noise on the long-time ageing dynamics of a quenched ferromagnetic spin system with a non-conserved order parameter and described through a Langevin equation with a thermal noise term and a disordered initial state is studied. If the noiseless part of the system is Galilei-invariant and scale-invariant with dynamical exponent z=2, the two-time linear response function is independent of the noise and therefore has exactly the form predicted from the local scale-invariance of the noiseless part. The two-time correlation function is exactly given in terms of certain noiseless three- and four-point response functions. An explicit scaling form of the two-time autocorrelation function follows. For disordered initial states, local scale-invariance is sufficient for the equality of the autocorrelation and autoresponse exponents in phase-ordering kinetics. The results for the scaling functions are confirmed through tests in the kinetic spherical model, the spin-wave approximation of the XY model, the critical voter model and the free random walk.

cond-mat.stat-mech↗
arXiv2004

Local scale-invariance in ageing phenomena

Many materials quenched into their ordered phase undergo ageing and there show dynamical scaling. For any given dynamical exponent z, this can be extended to a new form of local scale-invariance which acts as a dynamical symmetry. The scaling functions of the two-time correlation and response functions of ferromagnets with a non-conserved order parameter are determined. These results are in agreement with analytical and numerical studies of various models, especially the kinetic Glauber-Ising model in 2 and 3 dimensions.

cond-mat.stat-mech↗
arXiv2004

Dynamical space-time symmetry for ageing far from equilibrium

The dynamical scaling of ageing ferromagnetic systems can be generalized to a local scale invariance. This yields a prediction for the causal two-time response function, which has been numerically confirmed in the Glauber-Ising model quenched into the ordered phase. For a dynamical exponent z=2, a new embedding of the Schrödinger group into the conformal group and the resulting conditions for the validity of local scale invariance are discussed.

cond-mat.stat-mech↗
arXiv2004

Scaling of the linear response in simple ageing systems without disorder

The time-dependent scaling of the thermoremanent and zero-field-cooled susceptiblities in ferromagnetic spin systems undergoing ageing after a quench to a temperature at or below criticality is studied. A recent debate on their interpretation is resolved by showing that for systems with a short-ranged equilibrium spin-spin correlator and above their roughening temperature, the field-cooled susceptibility $χ_{\rm FC}(t)-χ_0\sim t^{-A}$ where $χ_0$ is related to the equilibrium magnetization and the exponent A is related to the time-dependent scaling of the interface width between ordered domains. The same effect also dominates the scaling of the zero-field-cooled susceptibility $χ_{\rm ZFC}(t,s)$, but does not enter into the thermoremanent susceptibility $ρ_{\rm TRM}(t,s)$. However, there may be large finite-time corrections to the scaling of $ρ_{\rm TRM}(t,s)$ which are explicitly derived and may be needed in order to extract reliable ageing exponents. Consistency with the predictions of local scale invariance is confirmed in the Glauber-Ising and spherical models.

cond-mat.stat-mech↗
arXiv2003

On the universality of the fluctuation-dissipation ratio in non-equilibrium critical dynamics

The two-time nonequilibrium correlation and response functions in 1D kinetic classical spin systems with non-conserved dynamics and quenched to their zero-temperature critical point are studied. The exact solution of the kinetic Ising model with Glauber dynamics for a wide class of initial states allows for an explicit test of the universality of the non-equilibrium limit fluctuation-dissipation ratio X_{\infty}. It is shown that the value of X_{\infty} depends on whether the initial state has finitely many domain walls or not and thus two distinct dynamic universality classes can be identified in this model. Generic 1D kinetic spin systems with non-conserved dynamics fall into the same universality classes as the kinetic Glauber-Ising model provided the dynamics is invariant under the C-symmetry of simultaneous spin and magnetic-field reversal. While C-symmetry is satisfied for magnetic systems, it need not be for lattice gases which may therefore display hitherto unexplored types of non-universal kinetics.

cond-mat.stat-mech↗
arXiv2003

Local scale invariance and its applications to strongly anisotropic critical phenomena

The generalization of dynamical scaling to local scale invariance is reviewed. Starting from a recapitulation of the phenomenology of ageing phenomena, the generalization of dynamical scaling to local scale transformation for any given dynamical exponent $z$ is described and the two distinct types of local scale invariance are presented. The special case $z=2$ and the associated Ward identity of Schrödinger invariance is treated. Local scale invariance predicts the form of the two-point functions. Existing confirmations of these predictions for (I) the Lifshitz points in spin systems with competing interactions such as the ANNNI model and (II) non-equilibrium ageing phenomena as occur in the kinetic Ising model with Glauber dynamics are described.

cond-mat.stat-mech↗
arXiv2003

The kinetic spherical model in a magnetic field

The long-time kinetics of the spherical model in an external magnetic field and below the equilibrium critical temperature is studied. The solution of the associated stochastic Langevin equation is reduced exactly to a single non-linear Volterra equation. For a sufficiently small external field, the kinetics of the magnetization-reversal transition from the metastable to the ground state is compared to the ageing behaviour of coarsening systems quenched into the low-temperature phase. For an oscillating magnetic field and below the critical temperature, we find evidence for the absence of the frequency-dependent dynamic phase transition, which was observed previously to occur in Ising-like systems.

cond-mat.stat-mech↗
arXiv2003

Schr"odinger invariance and space-time symmetries

The free Schrödinger equation with mass M can be turned into a non-massive Klein-Gordon equation via Fourier transformation with respect to M. The kinematic symmetry algebra sch_d of the free d-dimensional Schrödinger equation with M fixed appears therefore naturally as a parabolic subalgebra of the complexified conformal algebra conf_d+2 in d+2 dimensions. The explicit classification of the parabolic subalgebras of conf_3 yields physically interesting dynamic symmetry algebras. This allows us to propose a new dynamic symmetry group relevant for the description of ageing far from thermal equilibrium, with a dynamical exponent z=2. The Ward identities resulting from the invariance under conf_d+2 and its parabolic subalgebras are derived and the corresponding free-field energy-momentum tensor is constructed. We also derive the scaling form and the causality conditions for the two- and three-point functions and their relationship with response functions in the context of Martin-Siggia-Rose theory.

hep-th↗
arXiv2003

Scaling of the magnetic linear response in phase-ordering kinetics

The scaling of the thermoremanent magnetization and of the dissipative part of the non-equilibrium magnetic susceptibility is analysed as a function of the waiting-time $s$ for a simple ferromagnet undergoing phase-ordering kinetics after a quench into the ferromagnetically ordered phase. Their scaling forms describe the cross-over between two power-law regimes governed by the non-equilibrium exponents $a$ and $λ_R/z$, respectively. A relation between $a$, the dynamical exponent $z$ and the equilibrium exponent $η$ is derived from scaling arguments. Explicit tests in the Glauber-Ising model and the kinetic spherical model are presented.

cond-mat↗
arXiv2003

Reaction-diffusion processes and their connection with integrable quantum spin chains

This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly influenced through fluctuation effects in low dimensions which renders the habitual mean-field cinetic equations inapplicable. Starting from the master equation rewritten as a Schrödinger equation with imaginary time, the associated quantum hamiltonian of certain one-dimensional reaction-diffusion models is closely related to integrable magnetic chains. The relationship with the Hecke algebra and its quotients allows to identify integrable reaction-diffusion models and, through the Baxterization procedure, relate them to the solutions of Yang-Baxter equations which can be solved via the Bethe ansatz. Methods such as spectral and partial integrability, free fermions, similarity transformations or diffusion algebras are reviewed, with several concrete examples treated explicitly. An outlook on how the recently-introduced concept of local scale invariance might become useful in the description of non-equilibrium ageing phenomena is presented, with particular emphasis on the kinetic Ising model with Glauber dynamics.

cond-mat.stat-mech↗
arXiv2003

Ageing, dynamical scaling and conformal invariance

Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local free field theories. The scaling form of two-point functions is completely fixed by the requirement of local scale invariance. These predictions are confirmed through tests in the 3D ANNNI model at its Lifshitz point and in ageing phenomena of simple ferromagnets, here studied through the kinetic Ising model with Glauber dynamics.

cond-mat.stat-mech↗