Interacting Monomer-dimer Model Research Articles

Universality of the local persistence exponent for models in the directed Ising class in one dimension.

We investigate local persistence in five different models and their variants in the directed Ising (DI) universality class in one dimension. These models have right-left symmetry. We study Grassberger's models A and B. We also study branching and annihilating random walks with two offspring: the nonequilibrium kinetic Ising model and the interacting monomer-dimer model. Grassberger's models are updated in parallel. This is not the case in other models. We find that the local persistence exponent in all these models is unity or very close to it. A change in the mode of the update does not change the exponent unless the universality class changes. In general, persistence exponents are not universal. Thus it is of interest that the persistence exponent in a range of models in the DI class is the same. Excellent scaling behavior of finite-size scaling is obtained using exponents in the DI class in all models. We also study off-critical scaling in some models and DI exponents yield excellent scaling behavior. We further study graded persistence, which shows similar behavior. However, for a logistic map with delay, which also has the transition in the DI class, there is no transition from nonzero to zero persistence at the critical point. Thus the accompanying transition in persistence and universality of the persistence exponent hold when the underlying model has right-left symmetry.

Order–disorder transition in the two-dimensional interacting monomer-dimer model: Ising criticality

We study the order–disorder transition of the two-dimensional interacting monomer-dimer model (IMD) which has two symmetric absorbing states. To be self-contained, we first estimate numerically the dynamic exponent z of the two-dimensional Ising model. From the relaxation dynamics of the magnetization at the critical point, we obtain , or , where and are exactly known exponents. We then compare the critical relaxation of the order parameter at the transition point of the IMD with that of the Ising model. We find that the critical relaxation exponent is in good agreement with the Ising model, unlike the recent claim by Nam et al (2014 J. Stat. Mech. P08011). We also claim that the Binder cumulant is not an efficient quantity to locate the order–disorder transition point of the model with two symmetric absorbing states.

Nonequilibrium critical dynamics of two dimensional interacting monomer-dimer model: non-Ising criticality

We investigate the nonequilibrium relaxation dynamics of an interacting monomer-dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is known to exhibit two nearby continuous transitions: the Z2 symmetry-breaking order-disorder transition and the absorbing transition with directed percolation criticality. We performed a more detailed analysis of our extensive simulations on bigger lattice systems which reaffirms that the symmetry-breaking transition exhibits a non-Ising critical behavior with β ≃ 0.149(2) and η ≃ 0.30(1) that are distinct from those values of a pure two dimensional Ising model. Finite size scaling of dimer density near the symmetry breaking transition gives logarithmic scaling (α = 0.0) which is consistent with the hyperscaling relation but the corresponding exponent of νB ≃ 1.37(2) exhibits a conspicuous deviation from the pure Ising value of 1. The value of dynamic critical exponent z, however, is found to be close to that of the kinetic Ising model as 1/z ≃ 0.466(5) from the relaxation of staggered magnetization (and also similar but slightly smaller values from coarsening).

Interacting monomer-dimer model with infinitely many absorbing states

We study a modified version of the interacting monomer-dimer (IMD) model that has infinitely many absorbing (IMA) states. Unlike previously studied models with IMA states, the absorbing states can be divided into two equivalent groups which are dynamically separated infinitely far apart. Monte Carlo simulations show that this model belongs to a directed Ising universality class like the ordinary IMD model with two equivalent absorbing states. To our knowledge, this model is the first model with IMA states which does not belong to the directed percolation (DP) universality class. The DP universality class can be restored in two ways, i.e., by connecting the two equivalent groups dynamically, or by introducing a symmetry-breaking field between the two groups.

Critical behavior of an absorbing phase transition in an interacting monomer-dimer model

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. Static and dynamic Monte Carlo simulations show that the critical behavior at the transition is different from the conventional directed percolation universality class but is consistent with that of the models with the mass conservation of modulo 2. The values of static and dynamic critical exponents are compared with those of other models. We also show that the directed percolation universality class is recovered when a symmetry-breaking field is introduced.

Dynamic scaling behavior of an interacting monomer-dimer model.

We study the dynamic scaling behavior of 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. This transition does not belong to the conventional directed percolation universality class. The values of dynamic scaling exponents are estimated by Monte Carlo simulations for two distinct initial configurations, one near an absorbing state and the other with an interface between two different absorbing states. We confirm that the critical behavior is consistent with that of the models with the mass conservation of modulo 2.

Critical behavior of an interacting monomer-dimer model.

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.