Fulco UL, Messias DN, Lyra ML. Critical behavior of a one-dimensional diffusive epidemic process.
Phys Rev E Stat Nonlin Soft Matter Phys 2001;
63:066118. [PMID:
11415184 DOI:
10.1103/physreve.63.066118]
[Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2000] [Revised: 03/07/2001] [Indexed: 05/23/2023]
Abstract
We investigate the critical behavior of a one-dimensional diffusive epidemic propagation process by means of a Monte Carlo procedure. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants D(A) and D(B), respectively. According to a Wilson renormalization calculation, the system presents a second-order phase transition between a steady reactive state and a vacuum state, with distinct universality classes for the cases D(A)=D(B) and D(A)<D(B). A first-order transition has been conjectured for D(A)>D(B). In this work we perform a finite size scaling analysis of order parameter data at the vicinity of the critical point in dimension d=1. Our results show no signature of a first-order transition in the case of D(A)>D(B). A finite size scaling typical of second-order phase transitions fits well the data from all three regimes. We found that the correlation exponent nu=2 as predicted by field-theoretical arguments. Estimates for beta/nu are given for all relevant regimes.
Collapse