ICAM Themes
Professor A. Castro-Neto
University of California at Riverside
Department of Physics
900 University Avenue
Riverside CA 92521
(909) 787-6469
I would like to express my enthusiastic support for the Institute for Complex Adaptive Matter (ICAM) and congratulate you for this marvelous initiative. The objective of this letter is to propose a topic for the Workshop which will take place in December.
Cooperative phenomena is ubiquitous to condensed matter physics and biophysics. The interaction between the parts of a system with large number of degrees of freedom leads to new phenomena which is characterized by collective behavior. Collective behavior is a non-linear phenomenon involving a macroscopically large number of particles. Numerous examples of such collective behavior are observed in condensed matter physics (especially in phase transitions in magnetic and superconducting systems) and biophysics (such as in DNA replication).
The theory of second order phase transitions has seen an enormous development in the last decades due to the advent of the ideas of long range order and universality. These two concepts are in the heart of the physics of the renormalization group. While a lot is known about phase transitions in clean (ordered) systems less is known about the effect of disorder in systems close to criticality. With the development of new materials involving U and Ce intermetallics a new class of systems has been discovered. Some of these systems do not show long range magnetic order but usually are very close to an ordered state or the so-called quantum critical point (QCP). Moreover, these systems are very sensitive to external agents such as pressure, temperature, magnetic fields, disorder, etc. It is believed that this complex behavior to the external conditions is due to the presence of QCP. In these U and Ce systems the sensitivity due to the external conditions can be tracked down to the Kondo effect which is exponentially sensitive to lattice distortions and electronic densities. The competition between magnetic ordering and the Kondo effect in a disorder environment can lead to the so-called Griffiths singularities. These singularities are a clear example of the physics of rare events which can dominate completely the bulk properties of physical system. The change from usual uncorrelated (non-cooperative) to collective behavior is a strong crossover phenomena which can be described in terms of distributions of local susceptibilities. Griffiths singularities are, therefore, very general phenomenon which occurs in physical systems in the proximity of ordering due to the presence of strong but rare events.
Long range interactions are present in almost all phenonema in biology, chemistry and physics. Poor metals, like high temperature superconductors, probably cannot screen long range Coulomb interactions. Wigner crystals are stabilized by long range interactions. DNA is another example where long range correlations along the strain are very important due to its insulating behavior. Long range interactions in spin systems (such as RKKY) are the dominant interaction behind magnetic ordering in f-electrons compounds. Although long range interactions are more the rule than the exception our understanding of their effect in systems in physics, chemistry and biology is very limited. Recently developed numerical methods can be powerful tools in order to understand how long range interactions can lead to pattern formation and cooperative phenomena. Moreover, long range interactions lead to long range correlations and strong responses to external forces. I am very interested in this subject and in particular in how to treat long range interactions from the theoretical point of view in order to apply these ideas to experimentally relevant systems.