A cluster variation method approach to the problem of low-temperature statistics of a class of Ising models
Apstrakt
We Study the low-temperature thermodynamical and statistical properties of the ASYNNNI model, used to describe oxygen ordering in YBa2Cu3O6+2c. Analyzing the excited states we show that this model undergoes a second order phase transition at absolute zero temperature, From the divergence of the relative energy fluctuations, in the limit T -- GT 0, we deduce that for T approximate to 0 the deviation of the chemical potential it from its ground state value is linearly related to the partial derivative of the fraction of threefold coordinated Cu(1) ions it with respect to oxygen concentlation c. We use the cluster variation method (CVM) to determine the numerical value of the coefficient of this, relation and find that it is equal to - 1/2, independently of the values of the interaction parameters. This establishes a full equivalence between the ASYNNNI model and the one-dimensional Ising model, where the role of the nearest-neighbor interaction of the latter is played by the V-2 interact...ion in the former. We comment on the general applicability of low levels of the CVM approximation to systems equivalent to the one-dimensional Ising model.
Ključne reči:
YBa2Cu3O6+2c / ASYNNNI model / second order phase transition / cluster variation method / oxygen orderingIzvor:
Materials Transactions. JIM / Japan Institute of Metals, 2001, 42, 11, 2157-2164
DOI: 10.2320/matertrans.42.2157
ISSN: 1345-9678; 1347-5320
WoS: 000172844400004
Scopus: 2-s2.0-0035519419
Kolekcije
Institucija/grupa
VinčaTY - JOUR AU - Matić, Vladimir M. AU - Wille, LT AU - Lazarov, Nenad Đ. AU - Milić, Mirjana M. PY - 2001 UR - https://vinar.vin.bg.ac.rs/handle/123456789/2487 AB - We Study the low-temperature thermodynamical and statistical properties of the ASYNNNI model, used to describe oxygen ordering in YBa2Cu3O6+2c. Analyzing the excited states we show that this model undergoes a second order phase transition at absolute zero temperature, From the divergence of the relative energy fluctuations, in the limit T -- GT 0, we deduce that for T approximate to 0 the deviation of the chemical potential it from its ground state value is linearly related to the partial derivative of the fraction of threefold coordinated Cu(1) ions it with respect to oxygen concentlation c. We use the cluster variation method (CVM) to determine the numerical value of the coefficient of this, relation and find that it is equal to - 1/2, independently of the values of the interaction parameters. This establishes a full equivalence between the ASYNNNI model and the one-dimensional Ising model, where the role of the nearest-neighbor interaction of the latter is played by the V-2 interaction in the former. We comment on the general applicability of low levels of the CVM approximation to systems equivalent to the one-dimensional Ising model. T2 - Materials Transactions. JIM / Japan Institute of Metals T1 - A cluster variation method approach to the problem of low-temperature statistics of a class of Ising models VL - 42 IS - 11 SP - 2157 EP - 2164 DO - 10.2320/matertrans.42.2157 ER -
@article{ author = "Matić, Vladimir M. and Wille, LT and Lazarov, Nenad Đ. and Milić, Mirjana M.", year = "2001", abstract = "We Study the low-temperature thermodynamical and statistical properties of the ASYNNNI model, used to describe oxygen ordering in YBa2Cu3O6+2c. Analyzing the excited states we show that this model undergoes a second order phase transition at absolute zero temperature, From the divergence of the relative energy fluctuations, in the limit T -- GT 0, we deduce that for T approximate to 0 the deviation of the chemical potential it from its ground state value is linearly related to the partial derivative of the fraction of threefold coordinated Cu(1) ions it with respect to oxygen concentlation c. We use the cluster variation method (CVM) to determine the numerical value of the coefficient of this, relation and find that it is equal to - 1/2, independently of the values of the interaction parameters. This establishes a full equivalence between the ASYNNNI model and the one-dimensional Ising model, where the role of the nearest-neighbor interaction of the latter is played by the V-2 interaction in the former. We comment on the general applicability of low levels of the CVM approximation to systems equivalent to the one-dimensional Ising model.", journal = "Materials Transactions. JIM / Japan Institute of Metals", title = "A cluster variation method approach to the problem of low-temperature statistics of a class of Ising models", volume = "42", number = "11", pages = "2157-2164", doi = "10.2320/matertrans.42.2157" }
Matić, V. M., Wille, L., Lazarov, N. Đ.,& Milić, M. M.. (2001). A cluster variation method approach to the problem of low-temperature statistics of a class of Ising models. in Materials Transactions. JIM / Japan Institute of Metals, 42(11), 2157-2164. https://doi.org/10.2320/matertrans.42.2157
Matić VM, Wille L, Lazarov NĐ, Milić MM. A cluster variation method approach to the problem of low-temperature statistics of a class of Ising models. in Materials Transactions. JIM / Japan Institute of Metals. 2001;42(11):2157-2164. doi:10.2320/matertrans.42.2157 .
Matić, Vladimir M., Wille, LT, Lazarov, Nenad Đ., Milić, Mirjana M., "A cluster variation method approach to the problem of low-temperature statistics of a class of Ising models" in Materials Transactions. JIM / Japan Institute of Metals, 42, no. 11 (2001):2157-2164, https://doi.org/10.2320/matertrans.42.2157 . .