Editing Nicholas Metropolis (section)

==Monte Carlo method==
At Los Alamos in the late 1940s and early 1950s a group of researchers led by Metropolis, including [[John von Neumann]] and [[Stanislaw Ulam]], developed the [[Monte Carlo method]].<ref>Nicolas Metropolis.[http://lib-www.lanl.gov/la-pubs/00326866.pdf The Beginning of the Monte Carlo Method]. ''[[Los Alamos Science]]'', No. 15, Page 125.</ref><ref name="ENIAC">{{cite journal |last1=Haigh |first1=Thomas |last2=Priestley |first2=Mark |last3=Rope |first3=Crispin |title=Los Alamos Bets on ENIAC: Nuclear Monte Carlo Simulations, 1947-1948 |journal=IEEE Annals of the History of Computing |date=2014 |volume=36 |issue=3 |pages=42–63 |doi=10.1109/MAHC.2014.40 |s2cid=17470931 |url=https://ieeexplore.ieee.org/document/6880250|url-access=subscription }}</ref> This is a class of computational approaches that rely on repeated random sampling to compute their results, named in reference to Ulam's relative's love for the casinos of Monte Carlo. Metropolis was deeply involved in the very first use of the Monte Carlo method, rewiring the [[ENIAC]] computer to perform simulations of a nuclear core in 1948.<ref name="ENIAC"/> In 1953 Metropolis was credited as a co-author of a paper entitled ''[[Equation of State Calculations by Fast Computing Machines]]''.<ref name=metropolis>{{cite journal |author1=N. Metropolis |author2=A.W. Rosenbluth |author3=M.N. Rosenbluth |author4=A.H. Teller |author5=E. Teller  |name-list-style=amp |title=Equation of State Calculations by Fast Computing Machines |journal=Journal of Chemical Physics|volume=21|issue=6|pages=1087–1092|year=1953|doi=10.1063/1.1699114|bibcode = 1953JChPh..21.1087M |osti=4390578 |s2cid=1046577 |url=https://www.osti.gov/biblio/4390578 }}</ref> This landmark paper showed the first numerical simulations of a [[liquid]] and introduced a new Monte Carlo computational method for doing so.

In applications of the Monte Carlo method to problems in statistical mechanics prior to the introduction of the Metropolis algorithm, a large number of random configurations of the system would be generated, the properties of interest (such as energy or density) would be computed for each configuration, and then a [[weighted average]] computed where the weight of each configuration was its [[Boltzmann factor]], <math>e^{-E/kT}</math>, where <math>E</math> is the [[energy]], <math>T</math> is the [[temperature]], and <math>k</math> is the [[Boltzmann constant]]. The key contribution of the paper was the idea that

{{blockquote|Instead of choosing configurations randomly, then weighting them with exp(−''E''/''kT''), we choose configurations with a probability  exp(−''E''/''kT'') and weight them evenly.|Metropolis et al.|<ref name=metropolis />}}

The algorithm for generating samples from the [[Boltzmann distribution]] was later generalized by [[W.K. Hastings]] and has become widely known as the [[Metropolis–Hastings algorithm]].

In recent years a controversy has arisen as to whether Metropolis actually made significant contributions to the ''Equation of State Calculations ''paper.<ref>{{Cite journal |last=Gubernatis |first=J. E. |date=May 2005 |title=Marshall Rosenbluth and the Metropolis algorithm |url=https://zenodo.org/record/1231899 |journal=Physics of Plasmas |language=en |volume=12 |issue=5 |pages=057303 |doi=10.1063/1.1887186 |bibcode=2005PhPl...12e7303G |issn=1070-664X}}</ref>