The pair contact process with diffusion (PCPD) has been recently investigated extensively, but its critical behavior is not yet clearly established. By introducing biased diffusion, we show that the external driving is relevant and the driven PCPD exhibits a mean-field-type critical behavior even in one dimension. In systems which can be described by a single-species bosonic field theory, the Galilean invariance guarantees that the driving is irrelevant. The well-established directed percolation (DP) and parity conserving (PC) classes are such examples. This leads us to conclude that the PCPD universality class should be distinct from the DP or PC class. Moreover, it implies that the PCPD is generically a multi-species model and a field theory of two species is suitable for proper description.PACS numbers: 64.60. Ht,05.70.Ln,89.75.Da The steady state of an equilibrium system is characterized by its Hamiltonian and Gibbs measure. There is no systematic generalization to the stationary state of nonequilibrium systems so far. Since nonequilibrium systems encompass all kinds of many body systems without a constraint of detailed balance, it may be hopeless to find a universal formalism applied to general nonequilibrium systems. At this point, model studies or case-by-case studies are rather useful to accumulate our knowledge on nonequilibrium systems.Our experience on equilibrium systems illustrates the scale-free fluctuation or power law behavior at the critical point where the continuous phase change occurs. The scale-free nature is worth while to be studied not only because of its theoretical attraction, but also because of ubiquity in nature -the clustering of galaxies [1], 1/f noise [2], percolation structure [3], to name only a few. This scale-free nature is also expected at criticality under nonequilibrium circumstances. As a prototype of nonequilibrium critical phenomena, absorbing phase transitions (APTs) have been studied extensively [4]. APT is a transition from an active phase to an absorbing phase in nonequilibrium steady states. The absorbing states are defined as the configurations where the system cannot escape by the prescribed dynamic rules. As in equilibrium systems, this transition is possible only at the thermodynamic limit because the finite systems eventually fall into the absorbing states.In epidemiology, for example, the virus extinct state is an absorbing state. Actually, the disease spreading is modeled and dubbed the contact process (CP) by Harris [5]. CP shows a phase transition from the virus infested state (active state), to the quiescent state (absorbing state). This transition is known to belong to the directed percolation (DP) universality class. Actually, many types of models belong to the DP class and it is conjectured that a phase transition occurred in a system with a single absorbing state should share the critical behavior with the DP [6,7].As in equilibrium critical phenomena, a symmetry or conservation may play an important role in determining the universality class. Accor...

While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network, the suppressing tendency of the heterogeneity of the degree distribution, even for shorter characteristic path length, has also been reported. To see this, we investigate the effects of various factors such as the degree, characteristic path length, heterogeneity, and betweenness centrality on synchronization, and find a consistent trend between the synchronization and the betweenness centrality. The betweenness centrality is thus proposed as a good indicator for synchronizability.

A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the droplet-excitation (hyperscaling) argument, we conjecture the values of the FSS exponents for the Ising model, the susceptible-infected-susceptible model, and the contact process, all of which are confirmed reasonably well in numerical simulations.PACS numbers: 05.50.+q, 89.75.Hc, 89.75.Da, 64.60.Ht Critical phenomena in complex networks have attracted much attention recently and traditional models in statistical physics have been examined on diverse networks [1,2,3,4,5,6,7]. Interesting questions in such probes would be the existence of phase transitions and the network-dependent critical behavior near the transition. Up to now, various equilibrium systems such as Ising, Potts, and XY models [1,2,3,4] as well as nonequilibrium systems such as percolation [5], directed percolation [6], and synchronization models [7] have been studied by means of the mean-field (MF) approach [2], the replica method [3], and the thermodynamic potential hypothesis [1]. It is predicted that phase transitions in complex networks exhibit mostly the standard MF critical behavior except in highly heterogeneous scale-free (SF) networks where the interesting heterogeneity-dependent (but still MF-type) critical behavior appears [1,2,3].The MF prediction has been brought up to the test by extensive numerical simulations and passed it reasonably well in cases of less heterogeneous networks like random, small-world, and even some SF networks [4,5,6,7]. However, for the highly heterogeneous networks (like the most of SF networks found in nature), the asymptotic scaling regime could not be reached easily in numerical tests due to huge finite size effects and consequently there is no reasonably solid numerical analysis reported as yet. Therefore it is essential to understand the finite-size-scaling (FSS) behavior analytically in networks, not only to analyze numerical data for finite-size networks but also to explore the physics of correlated size scales in networks.In the present Letter, we propose a FSS theory for various models in complex networks, based on a dropletexcitation (hyperscaling) argument. Our conjecture for the FSS exponent values is confirmed via numerical simulations for the Ising model and the contact process [8].We first start with the standard FSS theory in low dimensional systems. As a typical example, consider the ferromagnetic Ising model. Its critical behavior near the transition is characterized by the singular behavior in the magnetization m ∼ ǫ β , the susceptibility χ ∼ |ǫ| −γ , and the correlation length ξ ∼ |ǫ| −ν , where ǫ is the reduced temperature defined by ǫ ≡ (T c − T )/T c .The standard FSS theory for the singular part of the free energy f reads [9]where b is the scale factor, d the spatial dimension, L the system linear size, and h the external field. The two scaling dimensions, y T ...

We study a monomer-dimer model with repulsive interactions between the same species in one dimension. With infinitely strong interactions the model exhibits a continuous transition from a reactive phase to an inactive phase with two equivalent absorbing states. Monte Carlo simulations show that the critical behavior is different from the conventional directed percolation universality class but seems to be consistent with that of the models with the mass conservation of modulo 2.

The effects of a stochastic reset, to its initial configuration, is studied in the exactly solvable one-dimensional coagulation-diffusion process. A finite resetting rate leads to a modified non-equilibrium stationary state. If in addition the input of particles at a fixed given rate is admitted, a competition between the resetting and the input rates leads to a non-trivial behaviour of the particle-density in the stationary state. From the exact inter-particle probability distribution, a simple physical picture emerges: the reset mainly changes the behaviour at larger distance scales, while at smaller length scales, the non-trivial correlation of the model without a reset dominates.

The entrainment transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite size effects leading to a correlation size exponentν = 5/2. Simulations of locally-coupled oscillators in d dimensions reveal two types of frequency entrainment: mean-field behavior at d > 4, and aggregation of compact synchronized domains in three and four dimensions. In the latter case, scaling arguments yield a correlation length exponent ν = 2/(d − 2), in good agreement with numerical results.

We present the theoretical study on non-equilibrium (NEQ) fluctuations for diffusion dynamics in high dimensions driven by a linear drift force. We consider a general situation in which NEQ is caused by two conditions: (i) drift force not derivable from a potential function and (ii) diffusion matrix not proportional to the unit matrix, implying non-identical and correlated multi-dimensional noise. The former is a well-known NEQ source and the latter can be realized in the presence of multiple heat reservoirs or multiple noise sources. We develop a statistical mechanical theory based on generalized thermodynamic quantities such as energy, work, and heat. The NEQ fluctuation theorems are reproduced successfully. We also find the time-dependent probability distribution function exactly as well as the NEQ work production distribution P (W) in terms of solutions of nonlinear differential equations. In addition, we compute low-order cumulants of the NEQ work production explicitly. In two dimensions, we carry out numerical simulations to check out our analytic results and also to get P (W). We find an interesting dynamic phase transition in the exponential tail shape of P (W), associated with a singularity found in solutions of the nonlinear differential equation. Finally, we discuss possible realizations in experiments.

We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over d-dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored analytically in the linear (strong-coupling) regime and numerically in the nonlinear (weak-coupling) regime. Our analysis shows that the oscillator phases are always desynchronized up to d = 4, which implies the lower critical dimension d P l = 4 for phase synchronization. On the other hand, the oscillators behave collectively in frequency (phase velocity) even in three dimensions (d = 3), indicating that the lower critical dimension for frequency entrainment is d F l = 2. Nonlinear effects due to periodic nature of limit-cycle oscillators are found to become significant in the weak-coupling regime: So-called runaway oscillators destroy the synchronized (ordered) phase and there emerges a fully random (disordered) phase. Critical behavior near the synchronization transition into the fully random phase is unveiled via numerical investigation. Collective behavior of globally-coupled oscillators is also examined and compared with that of locally coupled oscillators.