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The Time‐Dependent Ising Model on the 2D Penrose Lattice
Author(s) -
Doroba A.,
Sokalski K.
Publication year - 1991
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221670127
Subject(s) - glauber , ising model , spins , antiferromagnetism , lattice (music) , ferromagnetism , mean field theory , physics , mathematics , condensed matter physics , statistical physics , mathematical physics , quantum mechanics , acoustics , scattering
The kinetics of the Ising model on the 2D quasicrystal (Penrose) lattice is investigated. On the base of the Glauber method the system of the differential equations describing the temporal evolution of the expectation values of the averages of spins occupying the vertices of the Penrose “kite and dart” lattice is constructed. The mean field approximation, modified for the case of the nonperiodic system is applied. The stationary solution and their stability are discussed. The time‐dependent solutions of the problem in the case of the ferromagnetic and antiferromagnetic couplings between spins are found. The qualitative changes of the attractors under the changes of the external parameters are analysed. The limitations of applying the mean field approximation for the problems of the kinetics are discussed.