We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise on an equal footing. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. For a given tolerance parameter, the deviation from the Jarzynski equality depends onthe reduced coupling constant and the system size. In this work, we show that the deviation from the Jarzynski equality exhibits a universal scaling behavior inherited from the critical scaling laws of second-order phase transitions.
How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics?
We show that a multiple hit noise reduction technique involving the acceptance of only a fraction of the allowed atomistic deposition events could, by significantly suppressing the formation of high steps and deep grooves, greatly facilitate the identification of the universality class of limited mobility discrete solid-on-solid conserved nonequilibrium models of epitaxial growth. In particular, the critical growth exponents of the discrete one dimensional molecular beam epitaxy growth model are definitively determined using the noise reduction technique, and the universality class is establis…
We consider the non-equilibrium ferromagnetic transition of a mesoscopic sample of a resistive Stoner ferromagnet coupled to two paramagnetic leads. The transition is controlled by either the lead temperature T or the transport voltage V applied between the leads. We calculate the T and V dependence of the magnetization. For systems with a flat density of states we find within mean-field theory that even at finite bias the magnetization does not depend on the position along the sample axis, although the charge density and other quantities do vary. This may be relevant for possible spintronics …
We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface roughening in ideal molecular beam epitaxy. We find essentially all the earlier conclusions regarding the universality class of DT and WV models to be severely hampered by slow crossover and extremely long lived transient effects. We identify the correct asymptotic universality class(es) which differs from ea…
The critical behavior of driven lattice gas models has been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in the universality classes to which they belong. This is of paramount importance as it implies the question of whether or not a microscopic model and its mesoscopic field theory may possess different symmetries in nonequilibrium critical phenomena in contrast to their equilibrium counterparts. Here, we heat with finite rates two generic models of driven lattice gases across their resp…
The non-equilibrium dynamics of the three-dimensional Edwards-Anderson spin-glass model with different bond distributions is investigated by means of Monte Carlo simulation. A numerical method is used to determine the critical temperature and the scaling exponents of the correlation and the integrated response functions. The results obtained agree with those calculated in equilibrium simulations and suggest that the universality class does not depend on the exact form of the bond distribution.
We consider systems whose steady-states exhibit a nonequilibrium phase transition from an active state to one -among an infinite number- absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper critical dimension below which anomalous fluctuation driven scaling appears is d_c=6, in contrast to a widespread belief (see Dickman cond-mat 0110043 for an overview). We provide th…
Systems with absorbing (trapped) states may exhibit a nonequilibrium phase transition from a noise-free inactive phase into an ever-lasting active phase. We briefly review the absorbing critical phenomena and universality classes, and discuss over the controversial issues on the pair contact process with diffusion (PCPD). Two different approaches are proposed to clarify its universality issue, which unveil strong evidences that the PCPD belongs to a new universality class other than the directed percolation class.
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of phase transition and critical behaviour. Branching annihilating random walks with an even number of offspring (on the part of the ferromagnetic domain boundaries), is a decisive process in forming the steady state of the system for a range of parameters, in the family of models considered. A wide variety of quantities characterize the critical behaviour of the…
Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these res…
We study the nonequilibrium critical point of the zero temperature random field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random field Ising model belong to the same universality class. The physics of this curious…
The finite size analysis of the nonequilibrium phase transition, in two dimensional Ising ferromagnet driven by plane propagating magneticwave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamicphase transition from a high temperature dynamically symmetric ({\it propagating}) phase to a low temperature dynamically symmetry-broken ({\it pinned}) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth order Binder Cumulant of the dynamic order parameter as a fun…
This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynam…
We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit a continuous phase transition from an active phase into an absorbing phase which belongs to the universality class of the models with the parity conservation. However, when we break the symmetry between the absorbing states by introducing a symmetry-breaking field, Monte Carlo simulations show that the system goes back to the conventional directed percolation universality class. In terms of domain…
Nonequilibrium phase transitions between an active and an absorbing state are found in models of populations, epidemics, autocatalysis, and chemical reactions on a surface. While absorbing-state phase transitions fall generically in the DP universality class, this does not preclude other universality classes, associated with a symmetry or conservation law. An interesting issue concerns the dynamic critical behavior of models with an infinite number of absorbing configurations or a long memory. Sandpile models, the principal example of self-organized criticality (SOC), also exhibit absorbing- s…
We study analytically the role of initial conditions in nonequilibrium quantum dynamics considering the one-dimensional ferromagnets in the regime of spontaneously broken symmetry. We analyze the expectation value of local operators for the infinite-dimensional space of initial conditions of domain wall type, generally intended as initial conditions spatially interpolating between two different ground states. At large times the unitary time evolution takes place inside a light cone produced by the spatial inhomogeneity of the initial condition. In the innermost part of the light cone the form …
Models with a nonequilibrium wetting transition display a transition also in finite systems. This is different from nonequilibrium phase transitions into an absorbing state, where the stationary state is the absorbing one for any value of the control parameter in a finite system. In this paper, we study what kind of transition takes place in finite systems of nonequilibrium wetting models. By solving exactly a microscopic model with three and four sites and performing numerical simulations we show that the phase transition taking place in a finite system is characterized by the average interfa…
When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied trough Langevin equations or discrete growth models. In the first case, the Kardar-Parisi-Zhang equation, which defines a very robust universality class for nonequilibrium moving interfaces, with a soft-wall potential is considered. While in the second, microscopic models, in the corresponding universality class, with evaporation and deposition of particles in the presence of hard-wall are studied. Equilibrium wetting is related to a…
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 …
We investigate the finite temperature spin density wave (SDW) and charge density wave (CDW) transition of two-component lattice spinor Bose gases in optical lattices in the Mott-insulator limit. At the temperature scale around half of the on-site interaction energy, we find a new critical regime emerges and features, in particular, a new bicritical line and two critical lines associated with the finite temperature SDW-CDW, homogeneous-SDW, and homogeneous-CDW transition, respectively. Direct calculation of the critical exponents for the scaling behavior and investigating on the effective theor…
A generically observed mechanism that drives the self-organization of living systems is interaction via chemical signals among the individual elements -- which may represent cells, bacteria, or even enzymes. Here we propose a novel mechanism for such interactions, in the context of chemotaxis, which originates from the polarity of the particles and which generalizes the well-known Keller--Segel interaction term. We study the resulting large-scale dynamical properties of a system of such chemotactic particles using the exact stochastic formulation of Dean and Kawasaki along with dynamical renor…
We introduce an interface growth model exhibiting a nonequilibrium roughening transition (NRT). In the model, particles consist of two species, and deposit or evaporate on one dimensional substrate according to a given dynamic rule. When the dynamics is limited to occur on monolayer, this model has two absorbing states, belonging to the directed Ising (DI) universality class. At criticality, the density of vacant sites at the bottom layer in the growth model decays faster than the DI behavior, however, the dynamic exponent is close to the DI value, suggesting that the dynamics is related to th…
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed.…
Recently Carlon et. al. investigated the critical behavior of the pair contact process with diffusion [cond-mat/9912347]. Using density matrix renormalization group methods, they estimate the critical exponents, raising the possibility that the transition might belong to the same universality class as branching annihilating random walks with even numbers of offspring. This is surprising since the model does not have an explicit parity-conserving symmetry. In order to understand this contradiction, we estimate the critical exponents by Monte Carlo simulations. The results suggest that the trans…
We introduce the concept of dark space phase transition, which may occur in open many-body quantum systems where irreversible decay, interactions and quantum interference compete. Our study is based on a quantum many-body model, that is inspired by classical nonequilibrium processes which feature phase transitions into an absorbing state, such as epidemic spreading. The possibility for different dynamical paths to interfere quantum mechanically results in collective dynamical behavior without classical counterpart. We identify two competing dark states, a trivial one corresponding to a classic…
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 Fa…
As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in t…
When a classical system is driven through a continuous phase transition, its nonequilibrium response is universal and exhibits Kibble-Zurek scaling. We explore this dynamical scaling in the novel context of a three-dimensional topological magnet with fractionalized excitations, namely the liquid-gas transition of the emergent mobile magnetic monopoles in dipolar spin ice. Using field-mixing and finite-size scaling techniques, we place the critical point of the liquid-gas line in the three-dimensional Ising universality class. We then demonstrate Kibble-Zurek scaling for sweeps of the magnetic …
In bosonic gases at thermal equilibrium, an external quadratic drive can induce a Bose-Einstein condensation described by the Ising transition, as a consequence of the explicitly broken U(1) phase rotation symmetry down to $\mathbb{Z}_2$. However, in physical realizations such as exciton-polaritons and nonlinear photonic lattices, thermal equilibrium is lost and the state is rather determined by a balance between losses and external drive. A fundamental question is then how nonequilibrium fluctuations affect this transition. Here, we show that in a two-dimensional driven-dissipative Bose syste…
We analyse the universal properties of nonequilibrium steady states of driven Magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the dependence of various phenomenologically important dimensionless constants on the symmetries of the two-point correlation functions. We, for the first time, also suggest the intriguing possibility of multiscaling universality class varying continuously with certain dimensionless parameters. The experimental and theoretical implications of our results are discussed.
We investigate the critical behavior of systems exhibiting a continuous absorbing phase transition in the presence of a conserved field coupled to the order parameter. The results obtained point out the existence of a new universality class of nonequilibrium phase transitions that characterizes a vast set of systems including conserved threshold transfer processes and stochastic sandpile models.
We elucidate a non-conserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a non-zero noise cross-correlation of amplitude $D_\times$ in a stochastic Langevin description of the system, while maintaining the O(2) symmetry of the order parameter space. By performing dynamic renormalization group calculations in a field-theoretic set up, we analyze the ensuing nonequilibrium steady states and evaluate the scaling exponents near the critical point, which now depend explicitly on $D_\times$. Since the latter remains unrenormal…
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.
A biologically motivated model for spatio-temporal coexistence of two competing species is studied by mean-field theory and numerical simulations. In d>1 dimensions the phase diagram displays an extended region where both species coexist, bounded by two second-order phase transition lines belonging to the directed percolation universality class. The two transition lines meet in a multicritical point, where a non-trivial critical behavior is observed.
We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a dynamical phase transition that is obtained on tuning the initial conditions and demonstrate universality and characterize the critical behavior. The critical state is shown to be reached in a self-organized manner on dynamically evolving the diffusion equation subjected to a mirror symmmetry transformation.
Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems
Australian Institute of Bioengineering and Nanotechnology, The University of Queensland（澳大利亚生物工程和纳米技术研究所，昆士兰大学）；School of Chemistry, University of Melbourne（墨尔本大学化学学院）；Department of Physics, University of Mohaghegh Ardabili（莫哈杰格阿尔达比勒大学物理系）；School of Chemistry and Molecular Biosciences, The University of Queensland（昆士兰大学化学与分子生物学学院）；ARC Centre of Excellence for Green Electrochemical Transformation of Carbon Dioxide, The University of Queensland（昆士兰大学二氧化碳绿色电化转化卓越研究中心）
We reinvestigate the Deterministic Lattice Gas introduced as a paradigmatic model of the 1/f spectra (Phys. Rev. Lett. V26, 3103 (1990)) arising according to the Self-Organized Criticality scenario. We demonstrate that the density fluctuations exhibit an unexpected dependence on systems size and relate the finding to effective Langevin equations. The low density behavior is controlled by the critical properties of the gas at the absorbing state phase transition. We also show that the Deterministic Lattice Gas is in the Manna universality class of absorbing state phase transitions. This is in c…
We drive a $d$-dimensional Heisenberg magnet using an anisotropic current. The continuum Langevin equation is analysed using a dynamical renormalization group and numerical simulations. We discover a rich steady-state phase diagram, including a critical point in a new nonequilibrium universality class, and a spatiotemporally chaotic phase. The latter may be `controlled' in a robust manner to target spatially periodic steady states with helical order.
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation a…
We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation threshold of the lattice is characterized by unconventional activated (exponential) dynamical scaling and strong Griffiths effects. We calculate the critical behavior in two and three space dimensions, and we also relate our results to the recently found infinite-randomness fixed point in the disordered one-dimensional contact process.
It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale invariance, both near and far from thermal equilibrium. Part 1 introduces the response functional field theory representation of (nonlinear) Langevin equations. The RG is employed to compute the scaling exponents for several universality classes governing the critical dynamics near second-order phase transitions in equilibrium. The effects of reversible mode-coupling …
We study critical hysteresis in the random-field Ising model (RFIM) on a two-dimensional periodic lattice with a variable coordination number $z_{eff}$ in the range $3 \le z_{eff} \le 6$. We find that the model supports critical behavior in the range $4 < z_{eff} \le 6$, but the critical exponents are independent of $z_{eff}$. The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.
We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical percolation theory with the properties of the supercritical nonequilibrium system on a finite-size cluster. In the case of the contact process, the interplay between geometric criticality due to percolation and dynamical fluctuations of the nonequilibrium system leads to a new universality class. The critical point is characterized by ultraslow activated dy…
We study the effects of quenched extended impurities on nonequilibrium phase transitions in the directed percolation universality class. We show that these impurities have a dramatic effect: they completely destroy the sharp phase transition by smearing. This is caused by rare strongly coupled spatial regions which can undergo the phase transition independently from the bulk system. We use extremal statistics to determine the stationary state as well as the dynamics in the tail of the smeared transition, and we illustrate the results by computer simulations.
