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| Izergin, Anatoly Izergin | |
|---|---|
| Name | Anatoly Izergin |
| Birth date | 1940s |
| Birth place | Soviet Union |
| Nationality | Soviet Union; Russia |
| Fields | Theoretical physics; Statistical mechanics; Quantum field theory |
| Institutions | Landau Institute for Theoretical Physics; Moscow State University; Steklov Mathematical Institute |
| Alma mater | Moscow State University |
| Known for | Izergin–Korepin determinant; integrable models; quantum inverse scattering method |
Izergin, Anatoly Izergin was a Russian theoretical physicist noted for foundational work in exactly solvable models of statistical mechanics and integrable quantum field theory. He made key contributions to the theory of correlation functions, partition functions with domain-wall boundary conditions, and the algebraic Bethe ansatz, influencing developments related to the six-vertex model, XXZ spin chain, and quantum groups. Izergin's results connected rigorous methods from the Landau school to later advances by researchers working on the Yang–Baxter equation, Baxter's eight-vertex model, and modern integrability in mathematical physics.
Izergin studied physics and mathematics in the Soviet academic system, completing undergraduate and graduate studies at Moscow State University where he trained within circles that included scholars from the Landau Institute for Theoretical Physics, the Steklov Mathematical Institute, and collaborators influenced by Lev Landau and Evgeny Lifshitz. During his formative years he worked under advisors and mentors connected to the Soviet tradition exemplified by Isaak Khalatnikov, Alexei Abrikosov, and contemporaries in Moscow such as Ludvig Faddeev and Boris Izrailevich Kupershmidt. His doctoral work addressed problems in quantum statistical mechanics and scattering theory, aligning him with researchers in the Soviet school of theoretical physics including Anatoly Fomenko and Yakov Zeldovich.
Izergin held positions at major Soviet and Russian institutions, including long-term appointments at the Landau Institute for Theoretical Physics and teaching posts at Moscow State University and collaborations with the Steklov Mathematical Institute. He participated in seminars and research programs alongside figures from the Institute for Theoretical and Experimental Physics and international visitors associated with Princeton University, the Institute for Advanced Study, and research groups around Baxter-related integrability. Izergin attended and lectured at conferences convened by organizations such as the International Congress on Mathematical Physics and engaged with researchers from CNRS, Max Planck Institute for the Physics of Complex Systems, and University of Cambridge.
Izergin's research concentrated on exactly solvable models, the algebraic Bethe ansatz, and the analysis of correlation functions, producing techniques that linked the Yang–Baxter equation to explicit determinant formulae used in lattice models. He is best known for the Izergin determinant formula for the partition function of the six-vertex model with domain-wall boundary conditions, a result that bridged work by Rodney Baxter, Elliott Lieb, and Vladimir Korepin. His methods exploited algebraic structures related to quantum groups, the R-matrix formalism, and the Quantum Inverse Scattering Method pioneered by Ludvig Faddeev and others. Izergin collaborated with contemporaries such as Vladimir Korepin, producing results on form factors and correlation functions relevant to the XXZ spin chain, the Heisenberg model, and continuum limits connected to sine-Gordon model and nonlinear Schrödinger equation integrable theories.
His contributions include explicit determinant representations for scalar products and norms in Bethe eigenstates, and asymptotic analyses that connected to results by Tracy–Widom in random matrix theory and links to combinatorial structures studied by Percy MacMahon and Gessel. Izergin's work influenced later developments in the study of boundary conditions, the interplay with representation theory of Yangians and U_q(sl2), and applications in enumerative combinatorics, particularly alternating sign matrices and plane partitions where connections to Mills–Robbins–Rumsey conjectures emerged. His techniques have been applied in mathematical physics by researchers at institutions including Harvard University, University of Tokyo, and University of Oxford.
- I. G. Pronko and A. G. Izergin, "Correlation functions of the XXZ spin chain", Journal articles with derivations using the algebraic Bethe ansatz published in collaboration with authors linked to Vladimir Korepin and Nikolai Reshetikhin. - A. G. Izergin, "Partition function of the six-vertex model in a finite volume", work presenting the determinant formula later termed the Izergin determinant, circulated in contexts related to Rodney Baxter and Elliott Lieb. - A. G. Izergin and V. E. Korepin, papers on norms and scalar products for Bethe wavefunctions, cited in studies influenced by Ludvig Faddeev and Nikita Bogolyubov. - Reviews and lecture notes on integrable models prepared for seminars associated with the Landau Institute for Theoretical Physics and international schools attended by scholars from CERN, Mathematical Sciences Research Institute and Institute for Advanced Study.
Izergin received recognition within the Soviet and Russian scientific communities, including institutional awards from the Landau Institute for Theoretical Physics and honors tied to achievements in theoretical physics historically given by bodies such as the Russian Academy of Sciences and national science foundations. His results have been cited in prize-winning work by colleagues and his name endures in the eponymous determinant used across integrability literature, paralleling honors associated with figures like Lev Landau and Rodney Baxter in the field.
Izergin maintained a research-focused life connected to Moscow's mathematical physics community, collaborating with generations of scientists associated with Moscow State University, the Landau Institute for Theoretical Physics, and international centers of integrability. His legacy persists through the widespread use of the Izergin determinant in studies of exactly solvable models, influences on the algebraic Bethe ansatz, and the adoption of his methods by researchers in areas spanning statistical mechanics, quantum field theory, and combinatorics. Contemporary work at institutions such as Stony Brook University, University of California, Berkeley, and École Normale Supérieure continues to build on the frameworks he helped establish.
Category:Russian physicists Category:Theoretical physicists Category:20th-century physicists