In 1928 he went to the United States to take a faculty position at theJohns Hopkins University inBaltimore, Maryland. At JHU he had to teach freshman classes inchemistry, and it quickly became apparent that, while he was a genius at developing theories in physical chemistry, he had little talent for teaching. He was dismissed by JHU after one semester.[7]
On leaving JHU, he accepted a position (involving the teaching ofstatistical mechanics to graduate students in chemistry) atBrown University inProvidence, Rhode Island, where it became clear that he was no better at teaching advanced students than freshmen, but he made significant contributions to statistical mechanics andthermodynamics. His graduate studentRaymond Fuoss worked under him and eventually joined him on the Yale chemistry faculty. His statistical mechanics course was nicknamed "Sadistical Mechanics" by the students.[8]
His research at Brown was concerned mainly with the effects ondiffusion oftemperature gradients, and produced theOnsager reciprocal relations, a set of equations published in 1929 and, in an expanded form, in 1931, instatistical mechanics whose importance went unrecognized for many years. However, their value became apparent during the decades followingWorld War II, and by 1968 they were considered important enough to gain Onsager that year'sNobel Prize in Chemistry.
In 1933, when theGreat Depression limited Brown's ability to support a faculty member who was only useful as a researcher and not a teacher, he was let go by Brown. He traveled toAustria to visitelectrochemistHans Falkenhagen. He met Falkenhagen's sister-in-law, Margrethe Arledter. They were married on September 7, 1933, and had three sons and a daughter.[9]
After the trip toEurope, he was hired byYale University, where he remained for most of the rest of his life, retiring in 1972.[10]
At Yale, he had been hired as a postdoctoral fellow, but it was discovered that he had never received aPh.D.[3] While he had submitted an outline of his work in reciprocal relations to theNorwegian Institute of Technology, they had decided it was too incomplete to qualify as a doctoral dissertation. He was told that he could submit one of his published papers to the Yale faculty as a dissertation, but insisted on doing a new research project instead. His dissertation laid the mathematical background for his interpretation of deviations from Ohm's law in weak electrolytes.[11] It dealt with the solutions of theMathieu equation of period and certain related functions and was beyond the comprehension of thechemistry andphysics faculty. Only when some members of themathematics department, including the chairmanEinar Hille (who also likedA Course of Modern Analysis), insisted that the work was good enough thatthey would grant the doctorate if the chemistry department would not, was he granted a Ph.D. in chemistry in 1935.
Even before the dissertation was finished, he was appointed assistant professor in 1934,[3] and promoted to associate professor in 1940. He quickly showed at Yale the same traits he had at JHU and Brown: he produced brilliant theoretical research, but was incapable of giving a lecture at a level that a student (even a graduate student) could comprehend. He was also unable to direct the research of graduate students, except for the occasional outstanding one.[12] His two courses on statistical mechanics were nicknamed "Advanced Norwegian I" and "Advanced Norwegian II" for being incomprehensible.[8]
During the late 1930s, Onsager researched thedipole theory ofdielectrics, making improvements for another topic that had been studied by Peter Debye. However, when he submitted his paper to a journal that Debye edited in 1936, it was rejected. Debye would not accept Onsager's ideas until afterWorld War II. During the 1940s, Onsager studied thestatistical-mechanical theory ofphase transitions insolids, deriving a mathematically elegant theory which was enthusiastically received. In what is widely considered a tour de force of mathematical physics, he obtained the exact solution for the two dimensionalIsing model in zero field in 1944.[13][14][15]
In 1945, Onsager wasnaturalized as an American citizen, and the same year he was awarded the title ofJ. Willard Gibbs Professor of Theoretical Chemistry. This was particularly appropriate because Onsager, likeWillard Gibbs, had been involved primarily in the application ofmathematics to problems inphysics andchemistry and, in a sense, could be considered to be continuing in the same areas Gibbs had pioneered.In 1947, he was elected to theNational Academy of Sciences,[17] theAmerican Academy of Arts and Sciences in 1949,[18] and in 1950 he joined the ranks ofAlpha Chi Sigma.
In 1972 Onsager retired from Yale and became emeritus. He then became a member of theCenter for Theoretical Studies, University of Miami, and was appointed Distinguished University Professor of Physics.[21] At theUniversity of Miami he remained active in guiding and inspiring postdoctoral students as his teaching skills, although not his lecturing skills, had improved during the course of his career. He developed interests in semiconductor physics, biophysics and radiation chemistry. However, his death came before he could produce any breakthroughs comparable to those of his earlier years.
To solve the 2D Ising model, Onsager began by diagonalizing increasingly large transfer matrices. He said that it's because he had a lot of time during WWII. He began by computing the 2 × 2 transfer matrix of the 1D Ising model, which is already solved by Ising himself. He then computed the transfer matrix of the "Ising ladder", meaning two 1D Ising models side-by-side, connected by links. The transfer matrix is then 4 × 4. He repeated this for up to six 1D Ising models, resulting in transfer matrices of up to 64 × 64. He diagonalized all of them and found that all the eigenvalues were of a special form, so he guessed that the algebra of the problem was anassociative algebra (later called the Onsager algebra[22]).[23]
The solution involved generalized quaternion algebra and the theory of elliptic functions, which he learned fromA Course of Modern Analysis.[7]
He remained in Florida until his death from an aneurysm in Coral Gables, Florida in 1976. Onsager was buried next toJohn Gamble Kirkwood at New Haven'sGrove Street Cemetery. While Kirkwood's tombstone has a long list of awards and positions, including theAmerican Chemical Society Award in Pure Chemistry, the Richards Medal, and the Lewis Award, Onsager's tombstone, in its original form, simply said "Nobel Laureate". When Onsager's wife Gretel died in 1991 and was buried there, his children added an asterisk after "Nobel Laureate" and "*etc." in the lower right corner of the stone.[24] He was identified as a Protestant.[25]
TheNorwegian Institute of Technology established the Lars Onsager Lecture and The Lars Onsager Professorship in 1993 to award outstanding scientists in the scientific fields of Lars Onsager; Chemistry, Physics and Mathematics.[26] TheAmerican Physical Society establishedLars Onsager Prize in statistical physics in 1993. In 1997 his sons and daughter donated his scientific works and professional belongings toNTNU (before 1996NTH) inTrondheim,Norway as his alma mater. These are now organized asThe Lars Onsager Archive at theGunnerus Library in Trondheim.[27][28]
^Chen-Ning Yang,Selected papers (1945–1980) of Chen Ning Yang With Commentary, World Scientific Series in 20th Century Physics: Volume 36 (2005), paper and commentary [52a]. pp. 11-13
