2025-10-02 –, Coffee room
Language: English
Our package implements the parallel-tempering Monte Carlo method to study the thermodynamics of physical systems. Several copies of the system at different temperatures, randomly initialized, are evolved in parallel and allowed to exchange information of their current state. We make extensive use of Julia’s dynamic type system and multiple dispatch to unify implementations for different ensembles, interaction potentials and boundary conditions; multi-threading is used for parallelization.
We are studying solid-solid and solid-liquid phase transitions in atomic/molecular systems by means of the parallel tempering Monte Carlo method - also known as replica-exchange Markov chain Monte Carlo. In order to obtain the needed thermodynamic information several Markov chains of atomic/molecular configurations are generated simultaneously over the temperature range of interest. New configurations are generated by particle displacement, volume change or atomic exchange moves depending on the ensemble and system of choice. To prevent simulations at low temperatures to become stuck in local minima of the potential energy landscape, configurational exchanges between neighboring temperatures are attempted occasionally. New interesting regions in configurational space found at high temperatures where trajectories can move freely across potential barriers can thus be communicated “down” to lower temperatures. Energy histogram information is stored during the simulations and is checked for sufficient histogram overlap between neighboring temperatures to ensure the efficiency of the exchange mechanism.
Using Julia’s rich type system, we implemented different types of canonical and isobaric-isothermal ensembles with corresponding move strategies. Interaction potentials from extended Lennard Jones potentials, look-up tables to embedded-atom models are already implemented and an interface to a Fortran implementation of an atomic neural network potential exists. Besides the histogram information, radial distribution functions, sampled configurations and exchange statistics are stored.
We are also developing a Julia tool box for post-processing of the simulation results. At present we are using a multi-histogram analysis for calculation of the partition function allowing access to accurate internal energy, entropy and heat capacity information. Further, we are implementing structural analysis methods to get insight into how efficient configurational space is explored. For this, we perform energy minimization of atomic configurations saved during our simulations followed by a common-neighbor analysis and cluster similarity measures. The similarity scores allow for a compact visualization of the configurational space sampled and can be compared with a corresponding visualization of the potential energy surface gained by the basin-hopping algorithm.
After a short introduction of the Monte Carlo method we will present our implementation strategy while showcasing melting simulations for small neon clusters in strong magnetic fields and bulk argon under extremely high pressures.
I originally studied chemistry in Heidelberg, Germany gaining a PhD in Theoretical Chemistry. My extended postdoc time was spent in the US, back in Germany (Dresden) and then at Massey University Albany, transitioning more and more into physics while also taking care of and time off for the education of my children. I am now a Senior Lecturer in physics at the University of Auckland. My research lies in computational modelling from more fundamental topics like melting of matter in extreme conditions or exploring ground and excited states of quantum phases to more applied modelling of percolating carbon-elastomer composites.