Leipzig researchers develop new algorithm to study long-range interactions

At Leipzig University, researchers have devised an efficient method to study systems with long-range interactions, which were previously challenging to comprehend. These systems, like gases and magnets, have atoms interacting not only with their neighbors but also over long distances.

Professor Wolfhard Janke and his team use Monte Carlo computer simulations, generating random system states to uncover desired properties. Their new algorithm drastically reduces simulation time from centuries to mere days, providing profound insights into phase transitions' physics.

Equilibrium in a physical system means its macroscopic properties remain constant over time, while nonequilibrium processes occur when environmental changes push the system out of balance, seeking a new equilibrium state. Understanding the role of long-range interactions in these processes is a growing focus for statistical physicists worldwide.

The curse of long-range interactions

In systems with short-range interactions, calculating the system's over time requires a linear increase in operations with the number of components. However, long-range interacting systems necessitate considering interactions with all components, even distant ones, resulting in quadratic runtime increase as the system size grows.

Led by Professor Janke, a team of scientists has made a breakthrough by restructuring the algorithm and utilizing innovative data structures. This reduces the algorithmic complexity significantly, leading to a massive decrease in time for large systems and enabling the of entirely new research questions.

New horizons opened

The article demonstrates the new method's efficient application to nonequilibrium processes in systems with long-range interactions. One example explores spontaneous ordering in “hot” systems, where ordered domains grow over time following an abrupt temperature drop until an equilibrium state is achieved.

An everyday scenario reflects this when hot steam from a shower condenses on a cold nearby window, forming droplets that increase in size. Controlled slower cooling rates in other cases lead to the formation of vortices and structures, relevant in and solid state physics.

Furthermore, researchers have successfully used the algorithm to study phase separation, where two types of particles spontaneously segregate. Such nonequilibrium processes have wide-ranging significance, from industrial applications to understanding biological systems' functioning.

Computer simulations, a vital pillar of modern physics, complement experiments and analytical approaches. Many physics issues can only be addressed approximately or not at all through analytical methods, while experiments can be complex and time-consuming. In recent decades, computer simulations have greatly contributed to comprehending various physical systems across a broad spectrum.

Source: Leipzig University

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