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2014-12-21T19:58:39Z

83.233.54.174: Undid revision 639065895 by 119.159.190.117 (talk)

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83.233.178.2: /* Full-frame fisheye */

'''Ernst Ising''' ({{IPA-de|ˈiːzɪŋ|lang}}; born May 10, 1900, [[Cologne]], [[Rhine Province|Rhine]], [[German Empire|Germany]] – May 11, 1998, [[Peoria, Illinois|Peoria]], [[Illinois]], [[United States|USA]]) was a German [[physicist]], who is best remembered for the development of the [[Ising model]]. He was a professor of physics at [[Bradley University]] until his retirement in 1976.<ref>{{cite journal|author=Stutz, Conley|author2=Williams, Beverly|title=Obituary: Ernst Ising|journal=Physics Today|date=March 1999|volume=52|issue=3|pages=106–108|url=http://www.physicstoday.org/resource/1/phtoad/v52/i3/p106_s1?bypassSSO=1|doi=10.1063/1.882538}}</ref>

==Life==

Ernst Ising was born in Cologne in 1900. After school, he studied physics and mathematics at the [[University of Göttingen]] and [[University of Hamburg]]. In 1922, he began researching ferromagnetism under the guidance of [[Wilhelm Lenz]]. He earned a Ph.D in [[physics]] from the [[University of Hamburg]] in 1924 when he published his doctoral thesis (an excerpt or a summary of his doctoral thesis was published as an article in a scientific journal in 1925 and this has led many to believe that he published his full thesis in 1925, see,<ref>http://www.hs-augsburg.de/~harsch/germanica/Chronologie/20Jh/Ising/isi_intr.html</ref><ref>http://www.physik.tu-dresden.de/itp/members/kobe/isingconf.html</ref><ref>http://www.hs-augsburg.de/~harsch/anglica/Chronology/20thC/Ising/isi_fm00.html</ref>). His doctoral thesis studied a problem suggested by his teacher, Wilhelm Lenz. He investigated the special case of a linear chain of [[magnetic moment]]s, which are only able to take two positions, "up" and "down," and which are coupled by interactions between nearest neighbors. Mainly through following studies by [[Rudolf Peierls]], [[Hendrik Kramers]], [[Gregory Wannier]] and [[Lars Onsager]] the model proved to be successful explaining phase transitions between [[ferromagnetic]] and [[paramagnetic]] states.<ref name="stutz">{{cite journal|last1 = Stutz|first1 = Conley|last2 = Williams|first2 = Beverly|title = Ernst Ising (Obituary)|journal = [[Physics Today]]|volume = 52|issue = 3|pages = 106–108|publisher = American Institute of Physics|location = New York|year = 1999|month = 3|url = http://ptonline.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHTOAD000052000003000106000001&idtype=cvips|format = [[Portable Document Format|PDF]]|issn = 0031-9228|accessdate = 2009-01-09|doi = 10.1063/1.882538|bibcode = 1999PhT....52c.106S }}</ref><ref name="kobe">{{cite journal|last = Kobe|first = Sigismund|title = Ernst Ising 1900-1998|journal = [[Brazilian Journal of Physics]]|volume = 30|issue = 4|pages = 649–653|publisher = Sociedade Brasileira de Física|location = São Paulo|year = 2000|month = 12|url = http://www.sbfisica.org.br/bjp/Vol30/Num4/v30_649.pdf|format = [[Portable Document Format|PDF]]|issn = 0103-9733|accessdate = 2009-01-09|bibcode = 2000BrJPh..30..649K |doi = 10.1590/S0103-97332000000400003 }}</ref>

After earning his doctorate, Ernst Ising worked for a short time in business before becoming a teacher, in [[Salem, Baden-Württemberg|Salem]], [[Strausberg]] and [[Krosno Odrzańskie|Crossen]], among other places. In 1930, he married the economist Dr. Johanna Ehmer (February 2, 1902 - February 2, 2012). As a young German-Jewish scientist, Ising was barred from teaching and researching when [[Hitler]] came to power in 1933. In 1934, he found a position, first as a teacher and then as headmaster, at a Jewish school in [[Caputh, Brandenburg|Caputh]] near [[Potsdam]] for Jewish students who had been thrown out of public schools. Ernst and his wife Dr. Johanna Ising, née Ehmer, lived in Caputh near the famous summer residence of the Einstein family. In 1938, the school in Caputh was destroyed by the Nazis, and in 1939 the Isings fled to [[Luxembourg]], where Ising earned money as a shepherd and railroad worker. After the German [[Wehrmacht]] occupied Luxembourg, Ernst Ising was forced to work for the army. In 1947, the Ising family emigrated to the United States. Though he became Professor of Physics at [[Bradley University]] in [[Peoria, Illinois]], he never published again. Ising died at his home in Peoria in 1998, just one day after his 98th birthday.

==Work==
{{main|Ising model}}
The Ising model is defined on a discrete collection of variables called ''spins'', which can take on the value 1 or −1. The spins <math>S_i</math> interact in pairs, with energy that has one value when the two spins are the same, and a second value when the two spins are different.

The energy of the Ising model is defined to be:
:<math>
E = - \sum_{ij} J_{ij} S_i S_j
\,</math>

where the sum counts each pair of spins only once. Notice that the product of spins is either +1 if the two spins are the same (''aligned''), or −1 if they are different (''anti-aligned''). J is half the difference in energy between the two possibilities. Magnetic interactions seek to align spins relative to one another. Spins become randomized when thermal energy is greater than the strength of the interaction.

For each pair, if
::<math>J_{ij} > 0 </math> the interaction is called ''ferromagnetic''
::<math>J_{ij} < 0 </math> the interaction is called ''antiferromagnetic''
::<math>J_{ij} = 0 </math> the spins are ''noninteracting''

A [[ferromagnetic]] interaction tends to align spins, and an [[antiferromagnetic]] tends to antialign them.

The spins can be thought of as living on a [[graph theory|graph]], where each node has exactly one spin, and each edge connects two spins with a nonzero value of J. If all the Js are equal, it is convenient to measure energy in units of J. Then a model is completely specified by the graph and the sign of J.

The ''antiferromagnetic one-dimensional Ising model'' has the energy function:
:<math>
E = \sum_{i} S_{i} S_{i+1}
\,</math>
where i runs over all the integers. This links each pair of nearest neighbors.

In his 1924 PhD thesis, Ising solved the model for the 1D case. In one dimension, the solution admits no [[phase transition]]. On the basis of this result, he incorrectly concluded that his model does not exhibit phase behaviour in any dimension.

It was only in 1949 that Ising knew the importance his model attained in scientific literature, 25 years after his Ph.D thesis. Today, each year, about 800 papers are published that use the model to address problems in such diverse fields as neural networks, protein folding, biological membranes and social behavior.<ref name="stutz" /><ref name="sandia">{{cite web|url=http://www.sandia.gov/LabNews/LN04-21-00/sorin_story.html|title=Three-dimensional proof for Ising model impossible, Sandia researcher claims to have shown|publisher=Lab News, Sandia National Laboratories|first=Neil|last=Singer|accessdate=2008-02-27}}</ref>

==Notes==
{{Reflist}}

==External links==
* [http://www.hs-augsburg.de/~harsch/anglica/Chronology/20thC/Ising/isi_fm00.html Ernst Ising's 1924 PhD thesis] (English translation)
* [http://www.bradley.edu/las/phy/personnel/ising.html Article from Bradley University about Ising]
* {{MathGenealogy|id=115824}}

{{Persondata 
| NAME =Ising, Ersnt
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = German physicist
| DATE OF BIRTH = May 10, 1900
| PLACE OF BIRTH =
| DATE OF DEATH = May 11, 1998
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Ising, Ersnt}}
[[Category:German physicists]]
[[Category:1900 births]]
[[Category:1998 deaths]]

[[Category:People from Cologne]]
[[Category:People from Peoria, Illinois]]
[[Category:University of Göttingen alumni]]
[[Category:University of Hamburg alumni]]
[[Category:Bradley University faculty]]
[[Category:German emigrants to the United States]]

Category of groups

2012-08-22T13:41:03Z

83.233.149.188: Added adjoints, need interlinking

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2012-08-21T16:45:50Z

83.233.148.237: fixed/moved EL

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2012-08-16T19:05:20Z

83.233.11.80: /* References */ fix

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