Ernst Ising
Encyclopedia
Ernst Ising 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.
. 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 , ). 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.
After earning his doctorate, Ernst Ising worked for a short time in business before becoming a teacher, in Salem, Strausberg
and Crossen
, among other places. In 1930, he married the economist Dr. Johanna Ehmer
(born February 2, 1902). 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
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.
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:
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
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
, 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:
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.
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, who is best remembered for the development of the Ising model
Ising model
The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...
. He was a professor of physics at Bradley University
Bradley University
Bradley University, founded in 1897, is a private, co-educational university located in Peoria, Illinois. It is a small institution with an enrollment of approximately 6,100 undergraduate and postgraduate students and a full-time faculty of approximately 350....
until his retirement in 1976.
Life
Ernst Ising was born in Cologne in 1900. After school, he studied physics and mathematics at the University of Göttingen and University of HamburgUniversity of Hamburg
The University of Hamburg is a university in Hamburg, Germany. It was founded on 28 March 1919 by Wilhelm Stern and others. It grew out of the previous Allgemeines Vorlesungswesen and the Kolonialinstitut as well as the Akademisches Gymnasium. There are around 38,000 students as of the start of...
. In 1922, he began researching ferromagnetism under the guidance of Wilhelm Lenz. He earned a Ph.D in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
from the University of Hamburg
University of Hamburg
The University of Hamburg is a university in Hamburg, Germany. It was founded on 28 March 1919 by Wilhelm Stern and others. It grew out of the previous Allgemeines Vorlesungswesen and the Kolonialinstitut as well as the Akademisches Gymnasium. There are around 38,000 students as of the start of...
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 , ). His doctoral thesis studied a problem suggested by his teacher, Wilhelm Lenz
Wilhelm Lenz
Wilhelm Lenz was a German physicist, most notable for his invention of the Ising model and for his application of the Laplace–Runge–Lenz vector to the quantum mechanical treatment of hydrogen-like atoms.In 1906, Lenz graduated from the Klinger-Oberralschule, a non-classical secondary school...
. He investigated the special case of a linear chain of magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
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
Rudolf Peierls
Sir Rudolf Ernst Peierls, CBE was a German-born British physicist. Rudolf Peierls had a major role in Britain's nuclear program, but he also had a role in many modern sciences...
, Hendrik Kramers, Gregory Wannier
Gregory Wannier
Gregory Hugh Wannier was a Swiss physicist.He attended Princeton as a graduate student and later taught at several American universities before a stint in industry....
and Lars Onsager
Lars Onsager
Lars Onsager was a Norwegian-born American physical chemist and theoretical physicist, winner of the 1968 Nobel Prize in Chemistry.He held the Gibbs Professorship of Theoretical Chemistry at Yale University....
the model proved to be successful explaining phase transitions between ferromagnetic and paramagnetic states.
After earning his doctorate, Ernst Ising worked for a short time in business before becoming a teacher, in Salem, Strausberg
Strausberg
Strausberg is a city in Brandenburg, Germany, located 30 km east of Berlin. With a population of 26,206 in 2010 it is the largest town in the district of Märkisch-Oderland.-History:...
and Crossen
Krosno Odrzanskie
Krosno Odrzańskie is a city on the east bank of Oder River, at the confluence with the Bóbr. The town in Western Poland with 12,500 inhabitants is the capital of Krosno County...
, among other places. In 1930, he married the economist Dr. Johanna Ehmer
Jane Ising
Johanna "Jane" Ising is a former economics professor at Bradley University and wife of the physics professor Ernst Ising. She was born in Berlin, Germany and raised Lutheran. She earned a PhD in economics from the University of Berlin in 1926. She married Ernst Ising, a German Jew, on December...
(born February 2, 1902). 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
Caputh
Caputh is a village in the municipality of Schwielowsee, Potsdam-Mittelmark, Brandenburg, Germany.Caputh got a railway station in 1904...
near Potsdam
Potsdam
Potsdam is the capital city of the German federal state of Brandenburg and part of the Berlin/Brandenburg Metropolitan Region. It is situated on the River Havel, southwest of Berlin city centre....
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
Luxembourg
Luxembourg , officially the Grand Duchy of Luxembourg , is a landlocked country in western Europe, bordered by Belgium, France, and Germany. It has two principal regions: the Oesling in the North as part of the Ardennes massif, and the Gutland in the south...
, where Ising earned money as a shepherd and railroad worker. After the German Wehrmacht
Wehrmacht
The Wehrmacht – from , to defend and , the might/power) were the unified armed forces of Nazi Germany from 1935 to 1945. It consisted of the Heer , the Kriegsmarine and the Luftwaffe .-Origin and use of the term:...
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
Bradley University
Bradley University, founded in 1897, is a private, co-educational university located in Peoria, Illinois. It is a small institution with an enrollment of approximately 6,100 undergraduate and postgraduate students and a full-time faculty of approximately 350....
in Peoria, Illinois
Peoria, Illinois
Peoria is the largest city on the Illinois River and the county seat of Peoria County, Illinois, in the United States. It is named after the Peoria tribe. As of the 2010 census, the city was the seventh-most populated in Illinois, with a population of 115,007, and is the third-most populated...
, he never published again. Ising died at his home in Peoria in 1998, just one day after his 98th birthday.
Work
The Ising model is defined on a discrete collection of variables called spins, which can take on the value 1 or −1. The spins 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:
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
-
the interaction is called ferromagnetic
the interaction is called antiferromagnetic
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
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
, 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:
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
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
. 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.
External links
- Ernst Ising's 1924 PhD thesis (English translation)
- Article from Bradley University about Ising