Physicists have used a model commonly employed in the context of interacting particle systems to predict the behavior of voters in the past 30 U.S. presidential elections. Interestingly, the model they use is called the "Voter Model", but this is the first time it has been applied to real-world voters.The United States is the perfect forum for this sort of research as it has well-kept statistical records going back many years and is politically dominated by only two parties.
The model is a simple one that takes into account the influence of one's neighbors on the outcome of a decision. The researchers looked at population and commuting data for each county, taking into account that voters can be influenced both by the prevailing attitude in their home town and their workplace. For example, the probability of a Republican switching parties is related to the number of Democrats in her home county, the number of Democrats who commute to her county for work, and the number of Democrats in the county in which she works. The authors also added some noise terms (so they actually call this the "noisy voter model") to account for the many other factors influencing voters.
As it turns out, their results captured the true trends quite well, though the authors are quick to point out that their model serves to demonstrate some of the factors at work in the electoral decision-making process, not to predict election outcomes.
This article is short because theoretical physics papers are hard. If you want to try and wade through it yourself, the original study is available (free!) on arXiv: Is the Voter Model a model for voters?
If you'd rather read a summary written by someone more knowledgeable than myself, while also checking out some neat animations of the data, I enjoyed this article which I think is also free: Focus: Voter Model Works for US Elections