Matematik fizika va kompleks tahlilda o‘zaro bog‘liq ko‘plab nazariyalar mavjud bo‘lib, ular orasida Li-Yang teoremasi alohida o‘rin tutadi. Bu teorema statistik fizika vafazaviy o‘tishlar nazariyasida muhim rol o‘ynaydi. Polinomlarning kompleks tekislikdagi ildizlarini tahlil qilish orqali fizik tizimlarning xatti-harakatini o‘rganish imkonini beradi. Shuningdek, bu teorema fizikada termodinamik limit va holat o‘tishlarining nazariy asosi sifatida ko‘riladi. Li-Yang teoremasining asosiy ahamiyati, u kompleks o‘zgaruvchilar polinomining ildizlarini geometrik jihatdan chegaralaydi va statistik tizimlarning xususiyatlarini aniqlashga yordam beradi.Ushbu tadqiqotning asosiy maqsadi Li-Yang teoremasining n=2 va n=3 hollar uchun matematik isbotini batafsil keltirish va uning statistik fizika bilan bog‘liq ahamiyatini o‘rganishdan iboratdir.
Matematik fizika va kompleks tahlilda o‘zaro bog‘liq ko‘plab nazariyalar mavjud bo‘lib, ular orasida Li-Yang teoremasi alohida o‘rin tutadi. Bu teorema statistik fizika vafazaviy o‘tishlar nazariyasida muhim rol o‘ynaydi. Polinomlarning kompleks tekislikdagi ildizlarini tahlil qilish orqali fizik tizimlarning xatti-harakatini o‘rganish imkonini beradi. Shuningdek, bu teorema fizikada termodinamik limit va holat o‘tishlarining nazariy asosi sifatida ko‘riladi. Li-Yang teoremasining asosiy ahamiyati, u kompleks o‘zgaruvchilar polinomining ildizlarini geometrik jihatdan chegaralaydi va statistik tizimlarning xususiyatlarini aniqlashga yordam beradi.Ushbu tadqiqotning asosiy maqsadi Li-Yang teoremasining n=2 va n=3 hollar uchun matematik isbotini batafsil keltirish va uning statistik fizika bilan bog‘liq ahamiyatini o‘rganishdan iboratdir.
| № | Author name | position | Name of organisation |
|---|---|---|---|
| 1 | Ganixojayev N.N. | yetakchi ilmiy xodim | O’zbekiston Respublikasi Fanlar akademiyasi V.I.Romanovckiy nomidagi Matematika instituti |
| 2 | Tursunqulov A.A. | magistrant | Mirzo Ulug’bek nomidagi O’zbekiston Milliy universiteti, Toshkent, O’zbekiston |
| № | Name of reference |
|---|---|
| 1 | 1.Preston, Gibbs-states-on-countable-sets2.RIJEI.,IÆ, D. (1971 a). Extension of the Lee—Yang circle theorem. Phys. Rev. Lett. 26, 303-304.3.YANG, C. N. & LEE, T. D. (1952). Statistical theory of equations of state and phase transitions. Phys. Rev. 87, 404—4094.Fisher, M.E., Selke, W.: Phys. Rev. Lett. 44, 1502 (1980).5.R. Kindermann and J. L. Snell, Markov random fields and their applications (American Mathematical Society, Providence, RI, USA, 1980)6.SUOMELA, P. (1972). Factorings of finite dimensional distributions. Commentationes Physico-Mathematicae, 42, 1—137.Statistical Theory of Equations of State and Phase Transitions. 8.Theory of Condensation C. N. YANG AND T. D. LEE Institute for Advanced Study, Princeton, Kern Jersey (Received March 31, 1952)9.Lee Т. D., Yang С. N.. Statistical theory of equations of state and phase transitions I-II. "Phys. Rev.", 1952, v. 87, p. 404, 410;10.Xуанг К., Статистическая механика, пер. с англ., М.. 1966.М. В. Фейгелъман.11.Itzykson, Claude; Drouffe, Jean-Michel (1989),Statistical field theory. Vol. 1, Cambridge Monographs on Mathematical Physics,Cambridge University Press,ISBN978-0-521-34058-8,MR117517612.Knauf, Andreas (1999), "Number theory, dynamical systems and statistical mechanics",Reviews in Mathematical Physics,11(8):1027–1060,Bibcode:1999RvMaP..11.1027K,CiteSeerX10.1.1.184.8685,doi:10.1142/S0129055X99000325,ISSN0129-055X,MR171435213.Lee, T. D.; Yang, C. N. (1952), "Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model",Physical Review,87(3):410–419,Bibcode:1952PhRv...87..410L,doi:10.1103/PhysRev.87.410,ISSN0031-900714.Lieb, Elliott H.; Sokal, Alan D. (1981),"A general Lee-Yang theorem for one-component and multicomponent ferromagnets",Communications in Mathematical Physics,80(2):153–179, Bibcode:1981CMaPh..80..153L,doi:10.1007/BF01213009,ISSN0010-3616,MR0623156,S2CID5933204215.Newman, Charles M. (1974), "Zeros of the partition function for generalized Ising systems",Communications on Pure and Applied Mathematics,27(2):143–159,doi:10.1002/cpa.3160270203,ISSN0010-3640,MR048418416.Simon, Barry; Griffiths, Robert B. (1973),"The (φ4)2field theory as a classical Isingmodel",Communications in Mathematical Physics,33(2):145,164, Bibcode:1973CMaPh..33..145S,CiteSeerX10.1.1.210.9639,doi:10.1007/BF01645626,ISSN0010-3616,MR0428998,S2CID123201243 |