Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101487
Title: Local distributions of the 1D dilute Ising model
Authors: Panov, Y. D.
Issue Date: 2020
Publisher: Elsevier B.V.
Citation: Panov Y. D. Local distributions of the 1D dilute Ising model / Y. D. Panov. — DOI 10.1016/j.jmmm.2020.167224 // Journal of Magnetism and Magnetic Materials. — 2020. — Vol. 514. — 167224.
Abstract: The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types. © 2020 Elsevier B.V.
Keywords: CORRELATION FUNCTIONS
DILUTE ISING CHAIN
LOCAL DISTRIBUTIONS
MARKOV CHAIN
ANTIFERROMAGNETISM
DISTRIBUTION FUNCTIONS
GEOGRAPHICAL DISTRIBUTION
ISING MODEL
SPECIFIC HEAT
TEMPERATURE
ANTIFERROMAGNETICS
APPROXIMATE EQUATION
ASYMPTOTIC BEHAVIORS
CORRELATION LENGTHS
FINITE TEMPERATURES
LOCAL DISTRIBUTIONS
PAIR DISTRIBUTION FUNCTIONS
REGULAR MARKOV CHAIN
MARKOV CHAINS
URI: http://hdl.handle.net/10995/101487
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85088391170
PURE ID: 13383997
ae6714c2-0f7d-4bed-ac37-00fd3dc1cc6d
ISSN: 3048853
DOI: 10.1016/j.jmmm.2020.167224
metadata.dc.description.sponsorship: This work was supported by Program 211 of the Government of the Russian Federation, Agreement 02.A03.21.0006, and the Ministry of Education and Science of the Russian Federation, project FEUZ-2020-0054.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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