Andrej Srakar: Approximating the Ising model on fractal lattices of dimension two or greater than two

Datum objave: 12. 11. 2021
Seminar za verjetnost, statistiko in finančno matematiko
četrtek
18
november
Ura:
14.15
Lokacija:
Predavalnica 2.03 na FMF, Jadranska 21, Ljubljana.

V četrtek, 18. 11. 2021 ob14:15, bo v predavalnici 2.03 na FMF, Jadranska 21, potekalo predavanje Andreja Srakarja (EF) z naslovom Approximating the Ising model on fractal lattices of dimension two or greater than two.

Abstract: The exact solutions of the Ising model in one and two dimensions are well known, but much less is known about solutions on fractal lattices. In an important contribution, Codello, Drach and Hietanen (2015) construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two using a generalization of combinatorial method of Feynman (1972) and Vdovichenko (1965). We generalize their approach to fractal lattices of dimensions 2 and greater than 2, in particular of Koch curve variety (e.g. quadratic and von Koch surface). To this end we combine combinatorial optimization and transfer matrix approaches, referring to earlier works of Andrade and Salinas (1984). We compute approximate estimates for the critical temperatures and compare them to more usual Monte Carlo estimates. Similar as in Codello et al., we compute the correlation length as a function of the temperature and extract the relative critical exponent. The method allows generalizations to any fractal lattice, as well as concrete solutions to approach solutions for other non-translationally invariant lattices (e.g. those with random interactions).

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