The current state of Monte Carlo work on phase transitions and critical phenomena is reviewed. Both classical and quantum Monte Carlo results are discussed with emphasis on statistical lattice-model studies involving the highly accurate calculation of critical exponents. It is shown that finite-size scaling is an effective method whereby not only simple lattice models but also those of complex practical magnetic materials can be treated. For models allowing crossover phenomena, it is shown that both finite-size scaling theory and conventional power-law functions must be used in carrying out a Monte Carlo analysis.

PACS: 02.70.Lq, 64.60.−i, 75.40.−s, 75.50.−y (all) DOI: 10.1070/PU1999v042n07ABEH000498 URL: https://ufn.ru/en/articles/1999/7/d/ 000081866500004 Citation: Kamilov I K, Murtazaev A K, Aliev Kh K "Monte Carlo studies of phase transitions and critical phenomena" Phys. Usp. 42 689–709 (1999) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Камилов И К, Муртазаев А К, Алиев Х К «Исследование фазовых переходов и критических явлений методами Монте-Карло.» УФН 169 773–795 (1999); DOI: 10.3367/UFNr.0169.199907d.0773