New algorithm speeds up simulations of long-range interacting systems

At Leipzig University, a breakthrough method has been developed by Professor Wolfhard Janke and his team, allowing highly efficient investigations into systems with long-range interactions that previously puzzled experts. These systems, like gases and solid materials such as magnets, involve atoms interacting not just with neighbors but also over far distances.

The researchers employ Monte Carlo computer simulations, a stochastic process named after the Monte Carlo casino, to generate random system states. From these states, they can determine the desired properties and gain deep insights into the physics of phase transitions.

Remarkably, they’ve devised a new algorithm that completes these simulations in just days, a task that would have taken centuries with conventional methods. Their groundbreaking findings have been published in the esteemed journal Physical Review X.

In the realm of statistical physics, the focus is increasingly shifting towards nonequilibrium processes, where environmental changes force systems out of equilibrium, prompting them to seek new states of equilibrium. While much research has explored these processes in systems with short-range interactions, the role of long-range interactions is only beginning to be understood.

The curse of long-range interactions

In systems with short-range interactions, the time required to calculate the system’s evolution increases in a linear fashion with the number of components. However, for long-range interacting systems, each component must consider interactions with all others, even those far away, resulting in quadratic growth of runtime as the system size increases.

Fortunately, Professor Janke’s team of scientists has achieved a significant breakthrough by restructuring the algorithm and employing smart combinations of appropriate data structures. This reduction in algorithmic complexity dramatically cuts down on the computing time, particularly for large systems. As a result, entirely new questions can now be explored, thanks to the massive reduction in required computational resources.

New horizons opened

The article showcases the efficient application of the new method to nonequilibrium processes in systems with long-range interactions. One such example involves spontaneous ordering processes in a “hot” system, where ordered domains grow over time after an abrupt temperature drop until reaching an ordered equilibrium state.

Drawing from our daily experiences, think of taking a hot shower with a cold window nearby. You’ll notice droplets forming on the window as the hot steam rapidly cools down, causing the droplets to grow larger. Similarly, controlled slower cooling rates can lead to the formation of vortices and other structures, which are crucial in cosmology and solid-state physics.

Moreover, researchers have successfully utilized the algorithm to study phase separation, where two types of particles spontaneously separate. These nonequilibrium processes are vital in various fields, including industrial applications and understanding biological systems’ functioning.

Computer simulations stand as the third pillar of modern physics, complementing experiments and analytical approaches. Many physics issues can only be approached approximately or not at all using analytical methods. Experimental approaches can be challenging and time-consuming, requiring complex setups that may last for years. Computer simulations have thus significantly contributed to understanding a wide range of physical systems over the past decades.

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