scholarly journals CRITICAL BEHAVIOR OF AN EPIDEMIC MODEL OF DRUG RESISTANT DISEASES

2004 ◽  
Vol 15 (09) ◽  
pp. 1279-1290 ◽  
Author(s):  
C. R. DA SILVA ◽  
U. L. FULCO ◽  
M. L. LYRA ◽  
G. M. VISWANATHAN
Keyword(s):  
Critical Behavior ◽  
Finite Size ◽  
Universality Class ◽  
Active Phase ◽  
Propagation Model ◽  
Mutation Rates ◽  
Scaling Analysis ◽  
Directed Percolation ◽  
Drug Resistant ◽  
Finite Size Scaling

In this work, we study the critical behavior of an epidemic propagation model that considers individuals that can develop drug resistance. In our lattice model, each site can be found in one of the four states: empty, healthy, normally infected (not drug resistant) and strain infected (drug resistant) states. The most relevant parameters in our model are related to the mortality, cure and mutation rates. This model presents two distinct stationary active phases: a phase with co-existing normal and drug resistant infected individuals, and an intermediate active phase with only drug resistant individuals. We employed a finite-size scaling analysis to compute the critical points and the critical exponents, β/ν and 1/ν, governing the phase transitions between these active states and the absorbing inactive state. Our results are consistent with the hypothesis that these transitions belong to the directed percolation universality class.

THE RESTRICTED SPIN MODEL

1990 ◽  
Vol 04 (16) ◽  
pp. 1029-1041
Author(s):  
H.A. FARACH ◽  
R.J. CRESWICK ◽  
C.P. POOLE
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Heisenberg Model ◽  
Anisotropy Parameter ◽  
Finite Size ◽  
Universality Class ◽  
Spin Model ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Monte Carlo Calculations

We present a novel anisotropic Heisenberg model in which the classical spin is restricted to a region of the unit sphere which depends on the value of the anisotropy parameter Δ. In the limit Δ→1, we recover the Ising model, and in the limit Δ→0, the isotopic Heisenberg model. Monte Carlo calculations are used to compare the critical temperature as a function of the anisotropy parameter for the restricted and unrestricted models, and finite-size scaling analysis leads to the conclusion that for all Δ>0 the model belongs to the Ising universality class. For small A the critical behavior is clearly seen in histograms of the transverse and longitudinal (z) components of the magnetization.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR–PREY STOCHASTIC MODEL IN A 2D LATTICE

2010 ◽  
Vol 20 (02) ◽  
pp. 309-314 ◽  
Author(s):  
C. ARGOLO ◽  
H. OTAVIANO ◽  
IRAM GLERIA ◽  
EVERALDO ARASHIRO ◽  
TÂNIA TOMÉ
Keyword(s):  
Critical Behavior ◽  
Critical Exponents ◽  
Order Parameter ◽  
Species Coexistence ◽  
Finite Size ◽  
Universality Class ◽  
Square Lattice ◽  
Scaling Analysis ◽  
Predator Prey ◽  
Prey System

We investigate the critical behavior of a stochastic lattice model describing a predator–prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

Sign in / Sign up

Export Citation Format

Share Document