In December 2008, Journal of Mathematical Physics will publish a special issue on “Statistical Mechanics on Random Structures.” The Special Issue will be edited by:
Professor Pierluigi Contucci
Department of Mathematics
University of Bologna
Professor Cristian Giardinà
Department of Mathematics and Computer Science
TU Eindhoven
The Guest Editors have provided the following background for this Special Issue:
Three decades ago, Statistical Mechanics witnessed the introduction of disordered interactions in spin glass models.1 In addition to the description of condensed matter alloys, the proposed statistical mechanics formalism has proven to be an excellent method to study problems well beyond the original motivation and has indeed invaded fields as diverse as combinatorial optimization and neural networks. Interesting applications have been found in the biological, economical, and social sciences. Today, the rich mathematical structure of spin glasses is a leading research topic in probability theory,2 where it can be seen as a first attempt to introduce random interactions in particle systems. Diluted spin glasses have moved the theory toward adding a new source of randomness in the connectivity property of the interaction network like those of Erdös–Rényi random graphs. They are also relevant in computer science, since many random optimization problems are mapped in a natural way into the study of ground states of diluted mean-field spin glass models; for example, the K-sat model has been solved within the framework of “one-step replica symmetry breaking.”
Complex networks emerging in real systems (found in biology, social sciences, and internet and power grids) have revealed interesting properties of small world3 and scale free type,4 which led to an explosive development of the mathematical theory of random graphs.
The modeling of complex networks has given rise to a large number of random graphs models in which some correlations structure is introduced in the model, for example, the so-called “preferential attachment” type. To build a theory of interacting particles on random networks is a natural and necessary step to be pursued in the near future.
Most contributions will be invited, but submissions are welcome. All contributions will be reviewed by anonymous referees. The final authority for acceptance of papers is the Editor of Journal of Mathematical Physics (JMP).
All manuscripts should be submitted online via the JMP submission and peer review system. Hardcopy and e-mail submissions will not be allowed. To log into the online submission system, go to http:∕∕jmp.peerx-press.org. The cover letter should clearly state that the paper is intended for this special issue of the Journal. During the online submission process, authors should select “Special Issue” on the Category dropdown list and “Statistical Mechanics on Random Structures” on the Special Issue dropdown list of the manuscript submission form.
All submissions should be uploaded into the system no later than 1 June 2008.
