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| Alexander Izergin | |
|---|---|
| Name | Alexander Izergin |
| Birth date | 1947 |
| Birth place | Lviv, Ukrainian SSR |
| Death date | 2008 |
| Death place | Moscow, Russia |
| Fields | Mathematical physics, Quantum integrable systems, Statistical mechanics |
| Alma mater | Moscow State University, Landau School |
| Workplaces | Lomonosov Moscow State University, Steklov Institute of Mathematics |
| Known for | Izergin–Korepin method, Bethe ansatz adaptations, six-vertex model solutions |
Alexander Izergin was a Soviet and Russian mathematical physicist noted for foundational contributions to exactly solvable models in statistical mechanics, integrable quantum field theory, and the theory of correlation functions. His work linked algebraic techniques from the Quantum Inverse Scattering Method, representation theory related to the Yang–Baxter equation, and applications to models such as the six-vertex model, the XXZ model, and the Heisenberg model. Izergin's methods influenced later developments in the study of correlation functions, form factors, and determinantal representations used across mathematical physics and condensed matter theory.
Born in Lviv during the postwar period, Izergin completed secondary schooling before entering Moscow State University where he studied under mentors connected to the Landau School, the lineage of Lev Landau, Alexander Abrikosov, and Igor Tamm. He graduated from the Faculty of Physics, Moscow State University and pursued graduate research at the Steklov Institute of Mathematics under supervisors active in the community around the Soviet Academy of Sciences. During this period he interacted with researchers from Leningrad], [Moscow, collaborators from the Lebedev Physical Institute, and visitors associated with the Kurchatov Institute.
Izergin held positions at the Steklov Institute of Mathematics and later at Lomonosov Moscow State University, participating in seminar networks that included figures from the Landau Institute for Theoretical Physics, the Institute for Theoretical and Experimental Physics, and the Petersburg School of Mathematical Physics. He collaborated with contemporaries such as Vadim Korepin, Nikolai Bogoliubov, Ludvig Faddeev, Evgeny Sklyanin, and had interactions with researchers from Cambridge University, University of Oxford, Princeton University, IHÉS, and CNRS laboratories. Izergin visited conferences organized by International Congress of Mathematicians, European Physical Society, and workshops at CERN and Landau Institute where he presented on the Quantum Inverse Scattering Method and related algebraic techniques.
Izergin developed determinant representations for partition functions and correlation functions, most notably a determinant formula for the partition function of the six-vertex model with domain wall boundary conditions—often discussed alongside results by Vadim Korepin and building on the Bethe ansatz framework originating with Hans Bethe. He proved identities connected to the Yang–Baxter equation and advanced algebraic formulations linked to quantum groups and the R-matrix formalism introduced in works by Ludvig Faddeev and Miroslav Smirnov. His methods yielded exact expressions for scalar products and form factors relevant to the XXZ model and the Heisenberg model, influencing computations used in studies at Brookhaven National Laboratory, Bell Labs, Los Alamos National Laboratory, and in collaborations with teams at Stanford University and Harvard University. Izergin's approaches interfaced with techniques from Fredholm determinants, the Toda lattice, and asymptotic analysis methods developed in contexts such as the Riemann–Hilbert problem and the Deift–Zhou method.
Izergin received recognition from Soviet and Russian scientific institutions connected to the Soviet Academy of Sciences and later the Russian Academy of Sciences. His work was cited in prize considerations and commemorative sessions organized by the Landau Institute for Theoretical Physics, the Steklov Institute of Mathematics, and panels at the International Congress on Mathematical Physics. He was an invited speaker at conferences hosted by European Mathematical Society and honored in memorial volumes alongside colleagues such as Vadim Korepin, Ludvig Faddeev, and Nikolai Bogoliubov.
- A. G. Izergin, "Partition function of the six-vertex model in a finite volume," published in proceedings associated with Soviet Physics Doklady and later reprinted in collections linked to Steklov Institute of Mathematics seminars. - A. G. Izergin and V. E. Korepin, works on determinant formulae for scalar products, presented at meetings of the Landau Institute and included in archives of the Russian Mathematical Surveys. - Izergin contributions to compilations on the Quantum Inverse Scattering Method and lecture notes circulated through CERN and IHÉS programs. - Papers on form factors and correlation functions for the XXZ model and Heisenberg model in journals associated with the American Physical Society and European publishers.
Izergin balanced research with mentorship of students connected to Moscow State University and the Steklov Institute, influencing a generation of mathematical physicists who later joined institutions such as University of Cambridge, University of California, Berkeley, ETH Zurich, Max Planck Institute for Mathematics, and Perimeter Institute. His determinant techniques remain standard tools in studies at laboratories including CERN and in programs funded by bodies like the European Research Council and national science foundations. Memorial conferences at the Landau Institute and sessions at the International Congress on Mathematical Physics recalled his role alongside peers from Steklov Institute, Ludwig Maximilian University of Munich, Institute of Physics (Poland), and the Kiev Institute of Theoretical Physics. Category:Mathematical physicists