arXiv subjects

M. C. Marques

Publications and source records attributed to M. C. Marques.

4 recordsLinked to original sources

arXiv2002

Phase transition of a two dimensional binary spreading model

We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent singular behavior. The $N=3,4$ approximations result in a continuous phase transition belonging to a single universality class along the $D\in (0,1)$ phase transition line. Large scale simulations of the particle density confirmed mean-field scaling behavior with logarithmic corrections. This is interpreted as numerical evidence supporting that the upper critical dimension in this model is $d_c=2$.The pair density scales in a similar way but with an additional logarithmic factor to the order parameter. At the D=0 endpoint of the transition line we found DP criticality.

cond-mat.stat-mech↗

arXiv2001

Static critical behavior in the inactive phase of the pair contact process

Steady state properties in the absorbing phase of the $1d$ pair contact process (PCP) model are investigated. It is shown that, in typical absorbing states (reached by the system's dynamic rules), the density of isolated particles, $ρ_1$, approaches a stationary value which depends on the annihilation probability ($p$); the deviation from its 'natural' value at criticality, $ρ_1^{nat}$, follows a power law: $ρ_1^{nat}-ρ_1 \sim (p-p_c)^{β_1}$ for $p>p_c$. Monte Carlo simulations yield $β_1=0.81$. A cluster approximation is developed for this model, qualitatively confirming the numerical results and predicting $β_1=1$. The singular behavior of the isolated particles density in the inactive phase is explained using a phenomenological approach.

cond-mat↗

arXiv1998

A parity conserving dimer model with infinitely many absorbing states

We propose and study a model where, for the first time, two aspects are present: parity conservation and infinitely many absorbing states. Whereas steady-state simulations show that the static critical behaviour is not affected by the presence of multiple absorbing configurations, the influence of the initial state associated with the presence of slowly decaying memory effects is clearly displayed in time dependent simulations. We report results of a detailed investigation of the dependence of critical spreading exponents on the initial particle density.

cond-mat↗

arXiv1998

The relaxation of initial condition in systems with infinitely many absorbing states

We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations, relaxing to its natural value with the same power-law as the order parameter field. We argue that this slow relaxation, which was not taken into account in earlier studies of these models, is responsible for the continuously changing survival probability exponent. High precision numerical simulations show evidence of a(slight) dependence of the location of the transition point on the initial concentration, in the case of PCP. The damage spreading (DS) point and the spreading exponents coincide with those of the ordinary critical point in both cases.

cond-mat.stat-mech↗