Dynamic behavior of the 1D Ising ferromagnet with long-range interactions

EZEQUIEL V. ALBANO; DIEGO E. RODRIGUEZ; MARISA A. BAB

Punta del Este, Uruguay

Congreso; MEDYFINOL; 2008

Medyfinol 2008

 Ezequiel V. Albano, D. Rodríguez, M. Bab, Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina ealbano@inifta.unlp.edu.ar, ezequielalb@yahoo.com.arDynamic behavior of the 1D Ising ferromagnet with long-range interactionsThe dynamic behavior of the Ising model, with power-law decaying interactions of the form 1/rd + , is simulated ind = 1 dimension for = 0.75, by using the Monte Carlo method. This value of is selected because we expect thatcritical exponents will be far from both the mean-field values = 0.5 and the strong Kosterlitz-Thouless behavior.Both the standard relaxation of ordered configurations and the short-time dynamics of disordered configurationsare studied and rationalized in terms of scaling arguments. By measuring the time dependence of physicalobservables, such as the magnetization, susceptibility, Binder cumulant, correlation function, etc, the criticaltemperature and all the relevant critical exponents can be determined, including the static ( , , ) and the dynamic(z) ones. Also, the scaling exponent of the initial increase of the magnetization is evaluated. Based on this evidencewe conclude that the study of the dynamic behavior of the system allows the complete characterization of itscritical properties.(INVITED) Maximino Aldana, Instituto de Ciencias Físicas, UNAM, Morelos, Méxicomax@fis.unam.mx, maxaldana@yahoo.comCritical dynamics in genetic networks: examples from four kingdomsThe coordinated expression of the different genes in an organism is essential to sustain functionality under therandom external perturbations to which the organism might be subjected. To cope with such external variability,the global dynamics of the genetic network must possess two central properties. (a) It must be robust enough as toguarantee stability under a broad range of external conditions, and (b) it must be flexible enough to recognize andintegrate specific external signals that may help the organism to change and adapt to different environments. Thiscompromise between robustness and adaptability has been observed in dynamical systems operating at the brink ofa phase transition between order and chaos. Such systems are termed critical. Thus, criticality, a precise,measurable, and well characterized property of dynamical systems, makes it possible for robustness andadaptability to coexist in living organisms. In this talk investigate the dynamical properties of the genetranscription networks reported for S. cerevisiae, E. coli, and B. subtilis, as well as the network of segment polaritygenes of D. melanogaster, and the network of flower development of A. thaliana. By analyzing hundreds ofmicroarray experiments to infer the nature of the regulatory interactions among genes, and implementing thesedata into the Boolean models of the genetic networks, I will show that, to the best of the current experimentaldata available, the five networks under study indeed operate close to criticality. The generality of this resultsuggests that criticality at the genetic level might constitute a fundamental evolutionary mechanism thatgenerates the great diversity of dynamically robust living forms that we observe around us.