Researchers from the University of Leipzig have developed an algorithm that opens new possibilities in studying systems with far-acting interactions, such as gases and solid materials, which have posed difficulties for scientists. The algorithm, developed by Professor Wolfhard Yankke and his colleagues, uses Monte Carlo simulations for calculations. This stochastic approach creates random states of the system, allowing for a deeper understanding of the physics of phase transitions.
In systems where the elements only interact with their nearest neighbors, the volume of calculations increases linearly with the number of components. However, in systems with long-range interactions, where each element needs to consider all others, even those far away, the execution time increases quadratically.
The breakthrough came from Professor Yankke’s team, who reduced the computational complexity by restructuring the sequence and combination of data. This significantly reduced the operation time and allowed the researchers to focus on other issues. The findings of this research have been published in the journal Physical Review X.
The researchers demonstrated the applicability of the new method in nonequilibrium processes with long-range interactions. For example, they showed how the algorithm can be used to study the ordering of components after a sharp decrease in temperature. They also successfully applied the algorithm to study phase separation, where two types of particles spontaneously divide. These phenomena are important in various fields, including industry and the functioning of biological systems.
This discovery highlights the importance of computer simulations as a third pillar of modern science, alongside experiments and analytical approaches. Many problems in physics cannot be completely solved analytically, and experiments often require complex setups and long-term studies. Computer modeling has played a crucial role in advancing our understanding of a wide range of physical phenomena over the past decades.