Experiments by physicists in Konstanz prove Mermin-Wagner fluctuations
Now, 50 years later, a group of physicists from Konstanz headed by Dr Peter Keim, were able to prove the Mermin-Wagner theorem by experiments and computer simulations - at the same time as two international working groups from Japan and the USA. The research results were published in the 21 February 2017 edition of the Proceedings of the National Academy of Sciences (PNAS) scientific journal.
Microscopic image of lattice vibrations in a two-dimensional crystal consisting of a monolayer of approx. 6,500 colloids. Deviations of particle positions from ideal lattice sites can be observed. If these deviations grow (logarithmically) with the system size beyond all limits, they are due to Mermin-Wagner fluctuations. In a three-dimensional crystal, particle distances are fixed and deviations are limited, irrespective of the size of the crystal.
Credit: University of Konstanz
Based on a model system of colloids, Peter Keim was able to prove that in low-dimensional systems slow but steadily growing fluctuations occur in the distance between particles: the positions deviate from perfect lattice sites, distances frequently increase or decrease. Crystal formation over long ranges is therefore not possible in low-dimensional materials.
"Often the Mermin-Wagner theorem has been interpreted to mean that no crystals at all exist in two-dimensional systems. This is wrong: in fact long-wave density fluctuations grow logarithmically in two-dimensional systems and only destroy the order over long ranges," explains Peter Keim. In small systems of only a few hundred particles, crystal formation can indeed occur.
But the larger the systems, the more the irregularities in particle position grow, ultimately preventing crystal formation over long ranges. Peter Keim was also able to measure the growth rate of these fluctuations: he observed the predicted logarithmic growth, the slowest possible form of a monotonic increase. "However, the perturbation of the order not only has a structural impact, but also leaves traces in the dynamics of the particles," continues Keim.
The Mermin-Wagner theorem is one of the standard topics of interest in statistical physics and recently became a subject of discussion again in the context of the Nobel Prize for Physics: Michael Kosterlitz, the 2016 Nobel Prize winner published in a commentary how he and David Thouless got motivated to investigate so-called topological phase transitions in low-dimensional materials: it was the contradiction between the Mermin-Wagner theorem that prohibits the existence of perfect low-dimensional crystals, on the one hand and the first computer simulations that nevertheless indicated crystallization in two dimensions on the other hand. The proof from Peter Keim and his research team has now resolved this apparent contradiction: over short scales crystal formation is indeed possible, but impossible over long ranges.
The Konstanz-based project analyses data from four generations of doctoral theses. The Mermin-Wagner fluctuations were successfully proven by investigating the dynamics in unordered, amorphous, that means glassy, two-dimensional solids - just as in the work from Japan and the USA which appeared almost at the same time - while the existence of Mermin-Wagner fluctuations in two-dimensional crystals still has not been proven directly. The Konstanz research was sponsored by the German Research Foundation (DFG) and the Young Scholar Fund of the University of Konstanz.
Note to editors:
Photos can be downloaded from here:
Caption: Microscopic image of lattice vibrations in a two-dimensional crystal consisting of a monolayer of approx. 6,500 colloids. Deviations of particle positions from ideal lattice sites can be observed. If these deviations grow (logarithmically) with the system size beyond all limits, they are due to Mermin-Wagner fluctuations. In a three-dimensional crystal, particle distances are fixed and deviations are limited, irrespective of the size of the crystal.
Caption: Dr Peter Keim, University of Konstanz
Proceedings of the National Academy of Sciences (PNAS) 114, 1861 (2017)
Comments highlighting the original publication:
Proc. Natl. Acad. Sci. 114, 2440 (2017)
Nature Physics 13, 205 (2017)
University of Konstanz
Communication and Marketing
Phone: +49 753188-3603
Julia Wandt | EurekAlert!
Meteoritic stardust unlocks timing of supernova dust formation
19.01.2018 | Carnegie Institution for Science
Artificial agent designs quantum experiments
19.01.2018 | Universität Innsbruck
On the way to an intelligent laboratory, physicists from Innsbruck and Vienna present an artificial agent that autonomously designs quantum experiments. In initial experiments, the system has independently (re)discovered experimental techniques that are nowadays standard in modern quantum optical laboratories. This shows how machines could play a more creative role in research in the future.
We carry smartphones in our pockets, the streets are dotted with semi-autonomous cars, but in the research laboratory experiments are still being designed by...
What enables electrons to be transferred swiftly, for example during photosynthesis? An interdisciplinary team of researchers has worked out the details of how...
For the first time, scientists have precisely measured the effective electrical charge of a single molecule in solution. This fundamental insight of an SNSF Professor could also pave the way for future medical diagnostics.
Electrical charge is one of the key properties that allows molecules to interact. Life itself depends on this phenomenon: many biological processes involve...
At the JEC World Composite Show in Paris in March 2018, the Fraunhofer Institute for Laser Technology ILT will be focusing on the latest trends and innovations in laser machining of composites. Among other things, researchers at the booth shared with the Aachen Center for Integrative Lightweight Production (AZL) will demonstrate how lasers can be used for joining, structuring, cutting and drilling composite materials.
No other industry has attracted as much public attention to composite materials as the automotive industry, which along with the aerospace industry is a driver...
Scientists at Tokyo Institute of Technology (Tokyo Tech) and Tohoku University have developed high-quality GFO epitaxial films and systematically investigated their ferroelectric and ferromagnetic properties. They also demonstrated the room-temperature magnetocapacitance effects of these GFO thin films.
Multiferroic materials show magnetically driven ferroelectricity. They are attracting increasing attention because of their fascinating properties such as...
08.01.2018 | Event News
11.12.2017 | Event News
08.12.2017 | Event News
19.01.2018 | Materials Sciences
19.01.2018 | Health and Medicine
19.01.2018 | Physics and Astronomy