11 research outputs found
A globally accurate theory for a class of binary mixture models
Using the self-consistent Ornstein-Zernike approximation (SCOZA) results for
the 3D Ising model, we obtain phase diagrams for binary mixtures described by
decorated models. We obtain the plait point, binodals, and closed-loop
coexistence curves for the models proposed by Widom, Clark, Neece, and Wheeler.
The results are in good agreement with series expansions and experiments.Comment: 16 pages, 10 figure
Transições de fase sem termodinâmica
As aplicações de transições de fase vão muito além do contexto da termodinâmica de equilÃbrio, de onde surgiu. Nós revisamos um dos principais exemplos de uma transição de fase em um sistema sem termodinâmica, o processo de contato (PC), com ênfase no método de campo médio. Apresentamos um estudo de campo médio aplicado a um modelo para a transmissão da malária em uma população. Discutimos também as novas abordagens da distribuição quase-estacionária e o processo de contato conservativo
Critical Dynamics of the Contact Process with Quenched Disorder
We study critical spreading dynamics in the two-dimensional contact process
(CP) with quenched disorder in the form of random dilution. In the pure model,
spreading from a single particle at the critical point is
characterized by the critical exponents of directed percolation: in
dimensions, , , and . Disorder causes a
dramatic change in the critical exponents, to , , and . These exponents govern spreading following
a long crossover period. The usual hyperscaling relation, , is violated. Our results support the conjecture by Bramson, Durrett, and
Schonmann [Ann. Prob. {\bf 19}, 960 (1991)], that in two or more dimensions the
disordered CP has only a single phase transition.Comment: 11 pages, REVTeX, four figures available on reques
Theory of the NO+CO surface reaction model
We derive a pair approximation (PA) for the NO+CO model with instantaneous
reactions. For both the triangular and square lattices, the PA, derived here
using a simpler approach, yields a phase diagram with an active state for
CO-fractions y in the interval y_1 < y < y_2, with a continuous (discontinuous)
phase transition to a poisoned state at y_1 (y_2). This is in qualitative
agreement with simulation for the triangular lattice, where our theory gives a
rather accurate prediction for y_2. To obtain the correct phase diagram for the
square lattice, i.e., no active state, we reformulate the PA using sublattices.
The (formerly) active regime is then replaced by a poisoned state with broken
symmetry (unequal sub- lattice coverages), as observed recently by Kortluke et
al. [Chem. Phys. Lett. 275, 85 (1997)]. In contrast with their approach, in
which the active state persists, although reduced in extent, we report here the
first qualitatively correct theory of the NO+CO model on the square lattice.
Surface diffusion of nitrogen can lead to an active state in this case. In one
dimension, the PA predicts that diffusion is required for the existence of an
active state.Comment: 15 pages, 9 figure