Chapter 4 Critical worlds

Opalescent

Correlated and ordered

Classes of universality

Percolate

The forest is burning

Homogeneous nature

Referencias y comentarios:

· For phase diagrams of H20 and CO2: www.chemicalogic.com/download/phase_ diagram.html and www.chemguide.co.uk/physical/phaseeqia/phasediags.html.

· An excellent and classic reference for the theory of phase changes and critical phenomena in systems in equilibrium is

® Introduction to Phase Transitions and Critical Phenomena, H. Eugene Stanley (Clarendon Press; out of print, but accessible on the internet).

El comportamiento de funciones matemáticas en sus puntos críticos, que es relevante para comprender mejor el comportamiento de magnitudes físicas en los puntos críticos de diagramas (termodinámicos) de fase y en otros contextos, como se discute más adelante en este capítulo, se ilustra en descartes.cnice.mecd.es.

· An experiment that shows the phenomenon of critical opalescence is described in the web site www.physicsofmatter.com/notthebook/criticalopal/opalframe.html. Un fenómeno relacionado con la opalescencia crítica hace que predominen ciertas longitudes de onda en la luz que, proveniente del Sol, es dispersada por la atmósfera, lo que origina el color azul característico del cielo en condiciones normales, el color rojizo en los atardeceres, y el tono amarillento del disco solar. Para una explicación sencilla del color del cielo, puede verse enebro.pntic.mec.es.

· The simulation mentioned in class is described in detail in

® “Microscopic observations on a kinetic Ising model”, Raúl Toral and J. Marro, American Journal of Physics 54, 1114 (1986). Note that here the two spin states play the role of occupied/empty, dead/living, or A/B states in the models that we use in chapter 2 to understand other phenomenologies.

· A good general reference to percolation phenomena is

® Introduction to Percolation Theory, Dietrich Stauffer and Amnon Aharony (Taylor and Francis, Londres 1994).

For popular algorithms, see

® J. Hoshen and R. Kopleman, Physical Review B 14, 3438 (1976), and

® P. Leath, Physical Review B 14, 5056 (1976).

For interactive simulations: www.physics.buffalo.edu/gonsalves/java/percolation. html, pages.physics.cornell.edu/sethna/statmech/computerexercises/percolation/ percolation.html and www.physics.buffalo.edu/gonsalves/java/percolation.html.

A related Fermi’s paradox is in

® T. Kuiper and G.D. Brin, American Journal of Physics 57, 13 (1989). See also

® Complexity and criticality, Kim Christensen and Nicholas R Moloney (Imperial College Press, UK 2005).

· Simulation of forest fires, in www.sciencedaily.com/releases/1998/09/9809180709 16.htm and polymer.bu.edu/java/java/blaze/blazeapplet.html.

· On universality and renormalization, see the famous book by H Eugene Stanley quoted above and, by the same author,

® “Scaling, universality, and renormalization: Three pillars of modern critical phenomena”, H Eugene Stanley, Reviews of Modern Physics 71, S358 (1999). In the same journal, see the classical papers by Michael E. Fisher, 30, 615 (1967) and by Leo P. Kadanoff et al., 39, 395 (1967). Also interesting:

® “Renormalization group theory: the basis and formulation in statistical physics”, M.E. Fisher, Reviews of Modern Physics 70, 653 (1998);

® “Problems in Physics with Many Scales”, Kenneth G. Wilson, Scientific American 241, 158 (1979); and

® “Teaching the renormalization group”, Humphrey J. Maris and Leo P. Kadanoff, American Journal of Physics 46, 652 (1978).

Nota: véanse las referencias y enlaces que se incluyen en las dispositivas del curso, que a menudo completan las anteriores.