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Markov chain Monte Carlo
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=== Statistical Physics === Many contemporary research problems in statistical physics can be addressed by approximate solutions using Monte Carlo simulation, which provides valuable insights into the properties of complex systems. Monte Carlo methods are fundamental in computational physics, physical chemistry, and related disciplines, with broad applications including medical physics, where they are employed to model radiation transport for radiation dosimetry calculations.<ref>{{Cite journal |last1=Jia |first1=Xun |last2=Ziegenhein |first2=Peter |last3=Jiang |first3=Steve B. |date=2014-02-21 |title=GPU-based high-performance computing for radiation therapy |journal=Physics in Medicine and Biology |volume=59 |issue=4 |pages=R151β182 |doi=10.1088/0031-9155/59/4/R151 |issn=1361-6560 |pmc=4003902 |pmid=24486639|bibcode=2014PMB....59R.151J }}</ref><ref>{{Cite journal |last=Rogers |first=D. W. O. |date=July 2006 |title=REVIEW: Fifty years of Monte Carlo simulations for medical physics |url=https://ui.adsabs.harvard.edu/abs/2006PMB....51R.287R/abstract |journal=Physics in Medicine and Biology |language=en |volume=51 |issue=13 |pages=R287βR301 |doi=10.1088/0031-9155/51/13/R17 |pmid=16790908 |bibcode=2006PMB....51R.287R |issn=0031-9155}}</ref> Instead of exhaustively analyzing all possible system states, the Monte Carlo method randomly examines a subset of them to form a representative sample, and yields accurate approximations of the system's characteristic properties. As the number of sampled states increases, the error can be further reduced to a lower level.
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