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This field studies large systems of particles and uses statistical mechanics to investigate how particle interactions affect the system's behavior. We also research phase transitions and fundamental laws that govern atomic and molecular behavior, as well as large scale behaviour in wihch one may examine things such as clustering, mean-field behaviour and stability. Examples include Ising model, Voter models, exculsion models, percolation structures, and many more. Models with random environments can also be considered. These introduce an additional layer of randomness which influences the rates at which events or interactions occur, and present demanding mathematical challenges.