722 CHEMPHYSCHEM 2002, 3, 719 ±722

Optimization Algorithms inPhysics.By Alexander K. Hartmann and Heiko Rieger

Wiley-VCH, Berlin, 2001. 372 pp., hardcover �139–ISBN 3-527-40307-8

Quenched disorder, such as impurities orlattice defects, can have major effects onthe physical properties of materials. By™quenched∫, onemeans that the dis-order variables arefrozen on the timescale of the experi-ments and thus donot anneal away.The last ten yearshave seen greatprogress in our un-derstanding ofsuch disordered systems. This has beenpossible in part through the introductionof new computational tools for findingground states when the degrees of free-dom are discrete, Hartmann and Riegerbeing two of the main actors in this thrust.Their book gives a broad perspective ofthe associated optimisation algorithmsand also of the underlying physics issues.It will serve both as a guide and as areference manual for graduate studentsand more advanced researchers wantingto work in this field. Beyond that audi-ence, the book should also appeal toresearchers interested in Thomson's prob-lem, sphere packing, Lennard-Jonesatomic clusters or other continuous opti-misation problems. Indeed, the book at

large brings out the important physicsissues that can be studied by examiningground states and also it covers someheuristic optimisation methods; both ofthese themes go far beyond discreteoptimisation.

The book begins by introductory re-view chapters of complexity theory, stan-dard graph algorithms and statisticalphysics ; these make the book self-con-tained and accessible to most readers. Therest of the book is roughly divided intothree parts. Firstly, there are those modelsystems whose complexity is not too high,that is, for which the ground state can befound via a polynomial-time algorithm.Many of these very efficient algorithmsare associated with shortest paths ongraphs or maximum flows in networks.Model systems that fall into this class aredomain walls in disordered ferromagnets,the random-field Ising model, disorderedantiferromagnets in a field (DAFF) andvortex lattice problems. Secondly, thereare also the more difficult problems, forwhich one probably will never have suchefficient methods. In such systems, oneeither uses branch-and-bound type algo-rithms or resorts to heuristics, which arenot guaranteed to find the true optimum.The authors illustrate these methods onspin glasses (still a highly controversialsubject) and the vertex cover problem (acomputer science problem that isanalo-gous to some extent to a discrete versionof sphere packing).

In each of these chapters, the authorsexplain the state-of-the-art algorithms,first using high-level descriptions and

then giving some pseudo-code; they alsogive the central physical issues and pro-vide extensive bibliographical listings. Allthis makes clear the opportunities that arestill open and what tools are likely tomake further progress possible.

Finally, there is a third part to the book,in case you didn't gain your Ph.D. incomputational physics in the last fiveyears. Indeed, a 60 page chapter bringsyou up to date on the good ways tomanage a computational project, witheverything from programming tools andlibraries to data analysis and article prep-aration.

Let me stress that this book is con-ceived to be practical: there is an exten-sive index; no unnecessary formalism norabstractions are used; each chapter goesquickly to the essential issues and to thestate-of-the-art computational methods.Another point is that the book is self-contained except for the fact that nosource code is included; note howeverthat quite good optimisation codes arefreely available on the Web, and so themotivated reader should be able to getstarted quite quickly. Lastly, this bookfocuses on a still-evolving research fieldand so it cannot give a definitive cover-age; nevertheless, it should be useful forbeginners and practitioners alike.

Oliver MartinLaboratoire de Physique Theoriqueet Modeles Statistiques, UMR 8626, CNRSUniversite Paris-Sud91405 Orsay (France)Email : martino@ipno.in2p3.fr