Critical properties and phase transitions in probabilistic cellular automata and stochastic lattice gas model

• Grant number: 05/03237-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2007
• End date: June 30, 2008
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Tânia Tomé Martins de Castro
• Grantee: Everaldo Arashiro
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

We intend to do research in the area of nonequilibrium statistical mechanics, with the purpose of characterizing the kinetic phase transitions in irreversible models. In what follows we mention the main topics of this project: i) Obtainment of the critical behavior of the entropy production in stochastic lattice gas models; ii) Analysis of the dynamic properties of nonequilibrium systems in the short-time regime; iii) Investigation of the global persistence in models for helix formation in proteins. To accomplish these studies we will use methods of the statistical physics like Monte Carlo simulations and dynamic mean-field approximations. Bellow we briefly describe each topic of research. i) The entropy production will be analyzed in the stochastic formalism which describes it as an average over a stationary distribution. Our goal is to obtain the critical exponent associated to the entropy production by using Monte Carlo simulations and finite-size scaling hypothesis. We will study the entropy production in kinetic Ising models with competing dynamics. In this case, we will compare the obtained behavior with the singularity in the energy of the Ising equilibrium model defined in a square lattice. We expect that the critical properties of the entropy production will depend only on the symmetry of the dynamics and will not present a dependence on the dynamic critical exponent. Also, we will study the entropy production in irreversible models with the same symmetry of the equilibrium Potts model with n states. ii) We intend to examine the short-time behavior out of the order parameter correlation. We will focus our attention on the study of the dynamic properties of simplified models for protein formation. We will consider stochastic process which simulates the growing of a heteropolymer chain, as the HP model, with monomers of type H (hydrophobic) and P (polar). Also, we will verify the possibility of reproducing this growing by the consideration of the problem of self-avoiding walk in a square lattice. We intend to calculate the critical exponents of these models. We expect to be able to furnish more elements to characterize the phase transition in models for the formation of proteins. We will also analyze the critical properties of the ZGB model with desorption of particles. This is a lattice model which treats some of the aspects of oxidation of carbon monoxide over a catalytic surface. We expect to estimate with precision the dynamic exponent associated with the early time evolution of the carbon monoxide correlation in this model placed in the terminal critical point. iii) With the purpose of describing the helix-coil transition in polyamines we will study the probability of global persistence of the number of helix elements in proteins. This will be a continuity of the work that I have performed in my pH. D., where the helix-coil transition was studied from a short-time approach. In the present project, we expect to obtain the exponent of the global persistence in conformity with the universality class that we obtained before. (AU)