Phase transition of a two-dimensional binary spreading model

Abstract

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 subset (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 the bosonic field theoretical prediction 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 end point of the transition line we found directed percolation criticality.

Critical behavior of the one-dimensional diffusive pair contact process

“…The N = 3, 4 level cluster mean-field calculations confirmed a single mean-field universality class scenario similarly to the parity conserving version of this model [21]. Again the best conclusion one can draw from these data is that the N = 2 pair approximation is an odd one and we need at least N > 2 level of mean-filed to get the correct scaling behavior for binary production models.…”

“…This exponent is about 10% smaller than what was found in [16] but the two distinct class behavior seems to be supported. Although the upper critical dimension of PCPD is expected to be at d c = 2 [21] one may not exclude the possibility of a second critical dimension (d ′ c = 1) or topological effects in 1d that may cause logarithmic corrections to scaling. For this reason I tried to apply logarithmic fitting to the data of the form…”

“…Such kind of mean-field behavior is absent if we replace the annihilation AA → ∅ with coagulation AA → A [18]. By the investigation of the parity conserving version of the PCPD the mean-field and pair-mean-field approximations resulted in similar phase diagram, but higher order cluster mean-field showed a single mean-field class behavior [21] and the authors concluded that the for appropriate description of such binary production models at least N = 3 clusters are needed. That mean-field behavior was indeed found in d = d c = 2 by simulations [21].…”

“…Recently novel universal behavior is reported in some low-dimensional reaction-diffusion models featured by production at pairs and single particle diffusion [13][14][15][16][17][18][19][20][21]. In these systems the production compete with pair annihilation and diffusion.…”

Critical behavior in reaction-diffusion systems exhibiting absorbing phase transitions

“…In one dimensional, multicomponent reaction-diffusion systems site restriction turned out to be a relevant, new factor [13,14]. Global conservation laws by directed percolation and lattice gas models were shown to be irrelevant [15][16][17][18], while systems with multiple absorbing states [19] or with multi-components also exhibit DP class scaling behavior [20].Another important puzzle has been investigated intensively during the past three years that emerges at phase transitions of binary production reaction-diffusion systems [8,9,[20][21][22][23][24][25][26][27][28][29] (PCPD). In these systems particle production by pairs competes with pair annihilation and single particle diffusion.…”