On September 27, 2022, an era ended for us, and, as we believe, for the whole community of computational statistical physicists worldwide. After an enormously productive life, Kurt Binder passed away at the age of 78. We are deeply saddened that he is no longer with us.

We recall that once at a conference, the chairman introduced an oral contribution by him with the friendly, bantering words that the stage was open to “Mr. Monte Carlo.” And this is perhaps the shortest and most concise (but insufficiently comprehensive) way to characterize his impact. There are only few individuals in the history of science whose contribution to establishing Monte Carlo (MC) as a serious and remarkably versatile class of methods can be compared with his. When confining MC to its application in statistical physics, there is probably only one work that is even more important than his: The very establishment of the concept of importance sampling, and its realization through a Markov chain that satisfies detailed balance, first put forward in the 1953 groundbreaking work by Metropolis et al. While this initial ignition had provided the proof of principle, the world still had to wait one to two decades until the method was able to compete with other calculation schemes in statistical physics, such as series expansions, advanced Mean Field formalisms, closure approximations, and renormalization-group approaches. Kurt Binder was pivotal in transforming the early MC calculations (which produced, from the perspective of more established theoretical tools, little more than trivial additions) to a method that would generate qualitatively and quantitatively important new results with reliable error bars for numerical values. Kurt Binder was at the very beginning of this development and actually shaped the field in many respects.

We always admired Kurt Binder for his enormous, not to say fabulous, intellectual capacities, which comprised an extremely deep and broad understanding of most facets of statistical physics; a marvelous memory, which allowed him to simply quote bibliographic references directly from his brain; and an extremely organized way of thinking and expressing himself, in particular in writing, which then resulted in the ability to be very fast and efficient in producing his roughly 1200 publications—several of which were true groundbreaking milestones in the field. Indeed, his skills were by far not only confined to methodology. His deep physical insight guided him to pick problems in statistical physics where MC could make a difference, because more traditional approaches would notoriously fail, or, at least, encounter significant technical problems. The most prominent example of this remains the physics of second-order phase transitions, where erratic fluctuations defy traditional methods. In the late 60s, the theory of finite-size effects (or finite-size scaling) was established in order to understand how the finite extension of a sample would limit these fluctuations. Kurt Binder then realized that this was the key to analyzing MC data and consistently extrapolating to the thermodynamic limit. He thus developed the methods to systematically derive finite-size scaling relations for observables which are sampled in simulations, and, from there, to extract the universal properties. This became the method to calculate critical exponents and to check scaling laws, and, by roughly 1990, MC had beaten all other methods to accurately determine the universal properties of critical systems. Kurt Binder put forward the order parameter distribution as a particularly useful quantity to study, and introduced its fourth-order cumulant (now often simply referred to as “Binder parameter” or “Binder cumulant”) as a tool to accurately locate critical points. That said, we should emphasize that Kurt Binder never considered numerical accuracy as an end in itself, but always as a means in order to either comparatively demonstrate the usefulness of the method, or to answer subtle physical questions, which could arise from both theory and experiment.

Beyond making MC a reliable numerical tool to study statistical physics problems, Kurt Binder made substantial and important contributions in many sub-fields of statistical physics. He early on realized that the Monte Carlo process can be interpreted physically in a way that permits the investigation of dynamics. This was used, for example, to study spinodal decomposition (where he also showed that the concept of a spinodal is in reality an artifact of the Mean Field approximation), but also the dynamics of polymer systems, lattice gases and spin glasses. All this triggered many important experiments. In polymer physics, his work on phase separation in polymer blends is a prototype for critical behavior with a Mean Field to Ising crossover, governed by the degree of polymerization. This was first realized by Kurt Binder, and he formulated a Ginzburg criterion and checked it by careful computer simulations. Subsequent experiments on the unmixing of protonated and deuterated polystyrene nicely confirmed this work. Polymers are the only systems where such a crossover behavior is directly accessible and tunable without changing the basic interactions. Combining the above topics has led to a number of seminal contributions to calculating phase diagrams and studying the kinetics of nucleation phenomena and domain growth for systems ranging from classical metallic alloys to polymer-gas mixtures.

The physics of glasses and the glass transition was a theme which he kept on his agenda almost throughout his whole career. A particular highlight of his many studies on spin glasses was the demonstration that the two-dimensional Edwards–Anderson model does not exhibit a phase transition.

Finally, we would like to mention his many important contributions to surface physics, surface critical phenomena, and wetting. Together with Pierre Hohenberg, he developed a comprehensive description of critical behavior at surfaces, where new critical exponents were introduced. Later on, this work was “translated” to the adsorption of polymer chains. Both studies initiated detailed experiments. His numerous studies on wetting, capillary condensation, interface delocalization, and related phenomena were important counterparts to analytical studies based on effective interface Hamiltonians.

In his working style, he was the exact opposite of a “lonely thinker.” His collaborations were numerous and formed a network which spanned over the whole globe. Here, one particular personal and scientific friendship stood out, and this was his long and very fruitful collaboration with David P. Landau, which began in the mid-70s and lasted until the very end—on the day Kurt Binder passed away, David Landau was visiting Mainz. Perhaps a most important outcome of this transatlantic friendship was a highly successful textbook on MC methods. Furthermore, Kurt Binder was a first-class educator for 80 PhD students, at least 14 of whom later became professors, while in the classroom he would expose students to a wealth of material, such that they would appreciate early on what a rich and multi-faceted subject Theoretical Physics is.

Commensurate with his capabilities, his career path was very fast. Born on February 10, 1944, he was educated (both high school and university) in Vienna, where he obtained his PhD degree in 1969—already in his thesis he considered spin-spin correlations in ferromagnetic materials. He then stayed at the Technical University of Munich (1968-1974), IBM Rüschlikon (1972-1973), Bell Labs (1974), and then obtained his first professorship in Saarbrücken in fall 1974. In fall 1977, he moved to Forschungszentrum Jülich to become the head of the Theory 2 department, and then, in fall 1983, moved to the University of Mainz to establish the Condensed Matter Theory Group. He remained active there even after obtaining emeritus status in 2012—even until a few months before his death, when his deteriorating health forced him to withdraw from professional life.

For his achievements, Kurt Binder was honored by the community via numerous awards, most notably the Boltzmann Medal (2007). Further awards that may be mentioned include the Max Planck Medal of the German Physical Society (1993), the Berni Alder CECAM Prize (2001), the Lennard-Jones Medal (2009), and the APS Polymer Physics Prize (2020). He was very active in numerous bodies of scientific self-organization, including being a member of CECAM’s Scientific Advisory Committee, heading the DFG Collaborative Research Center 262 on the physics of glasses, chairing the IUPAP Commission on Thermodynamics and Statistical Physics, and various duties in managing the Jülich supercomputer center. Furthermore, he was an External Member of the Max Planck Institute for Polymer Research (Mainz), and a member of various academies (Austrian Academy of Sciences, German Academy of Sciences Leopoldina, Academy of Sciences and Literature Mainz). ISI honored him as a “Highly Cited Researcher.”

Having discussions with him was always inspiring. To many questions he could give clarifying and authoritative answers, often combined with useful hints to the literature, and sometimes with interesting anecdotes. This inspiration, however, went well beyond physics. As a typical member of his generation, he was highly interested in politics and liked to discuss such issues while being refreshingly outspoken. Quite often, his remarks were humorous and could be somewhat sarcastic—he once described himself as a big fan of Helmut Qualtinger, which clearly points to his Viennese background. Also, anyone who ever discussed science with Kurt Binder in his office, packed to the ceiling with papers and reprints, will never forget the typical situation, where he said “…and this has been published by xxx…”, went to one of the shelves and pulled the reprint mentioned out of a huge pile of different papers. It is probably these scientific and non-scientific exchanges that we will miss the most.

Burkhard Dünweg, Kurt Kremer, Friederike Schmid