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Lattice Models of Magnetic Polymers

Student: Vyacheslav Apasov

Supervisor: Evgeni Burovski

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Control Systems and Data Processing in Engineering (Master)

Year of Graduation: 2021

The main goal is to model a behaviour of spin subsystem on random walk without self-intersections in theta-transition phase. Swendsen-Wang and Wolff algorithms were implemented and then applied to one- and two-dimensional Ising lattice model and 3-state two-dimensional Potts model. Also, calculated main parameters of a model as energy, magnetization and heat capacity and shown their changes with temperature change. I did a research about convergence time of a model in different temperature intervals. Shown that models have different convergence time therefore, they behave as opposite substances in terms of magnetizations. Also shown, that in theta- transition phase model has a critical temperature value which is calculated withtin Binder’s cummulant approach. Conformation ensemble generated by self-avoiding walks was researched for Potts model as well.

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