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Critical behavior in anisotropic cubic systems with long-range interactions

Yoshitake Yamazaki

Physica A Statistical Mechanics and its ApplicationsMar 1, 19786 citations

Critical behavior of anisotropic cubic systems with long- and short-range interactions

Yoshitake Yamazaki, Arno Holz

Physica A Statistical Mechanics and its ApplicationsDec 1, 19812 citations

Critical behavior of N-component spin systems with random impurities in cubic-anisotropy crystalline material

Yoshitake Yamazaki, Moyuru Ochiai, Yoshiichi Fukuda +1 more

Physica A Statistical Mechanics and its ApplicationsSep 1, 19853 citations

Static and dynamic critical behavior of extended-defectN-component systems in cubic anisotropic crystals

Yoshitake Yamazaki, Arno Holz, Moyuru Ochiai +1 more

We study the static and dynamic critical behavior of N-component spin systems in crystals with cubic anisotropy in the presence of extended defects, namely ${\ensuremath{\epsilon}}_{d}$-dimensionally connected defects distributed randomly in d-${\ensuremath{\epsilon}}_{d}$ dimensions. These defects make the systems coordinate anisotropic. As a result of the presence of the cubic anisotropy and the coordinate anisotropy, various new types of critical behavior appear, e.g., an ${\ensuremath{\epsilon}}^{1/2}$ (\ensuremath{\epsilon}\ensuremath{\equiv}4-d) expansion for extended-defect XY systems, spiral trajectories, and oscillatory critical behavior for extended-defect systems, first-order phase transitions for extended-defect N-component systems with 2\ensuremath{\le}N<4 near the stability boundary of the free energy, and so on. The first two types of behavior will be investigated in detail.We study the static and dynamic critical behavior of N-component spin systems in crystals with cubic anisotropy in the presence of extended defects, namely ${\ensuremath{\epsilon}}_{d}$-dimensionally connected defects distributed randomly in d-${\ensuremath{\epsilon}}_{d}$ dimensions. These defects make the systems coordinate anisotropic. As a result of the presence of the cubic anisotropy and the coordinate anisotropy, various new types of critical behavior appear, e.g., an ${\ensuremath{\epsilon}}^{1/2}$ (\ensuremath{\epsilon}\ensuremath{\equiv}4-d) expansion for extended-defect XY systems, spiral trajectories, and oscillatory critical behavior for extended-defect systems, first-order phase transitions for extended-defect N-component systems with 2\ensuremath{\le}N<4 near the stability boundary of the free energy, and so on. The first two types of behavior will be investigated in detail.

Physical review. B, Condensed matterMar 1, 198624 citations

Critical behaviour of two-component spin systems with quenched random nonmagnetic impurities in cubic anisotropic crystals

Y. Yamazaki, M. Ochiai, Yoshiichi Fukuda

By means of the renormalisation-group approach, static and dynamic critical behaviours are studied for the XY spin system with cubic anisotropy and with quenched random nonmagnetic impurities. The stability of the quenched-random-impurity fixed point in d ( identical to 4- epsilon ) dimensions, the flow diagram of the interactions and the critical exponents are investigated, within the two-loop approximation, in terms of the epsilon 1/2 expansion. It is shown that the transition that appears is a first-order transition.By means of the renormalisation-group approach, static and dynamic critical behaviours are studied for the XY spin system with cubic anisotropy and with quenched random nonmagnetic impurities. The stability of the quenched-random-impurity fixed point in d ( identical to 4- epsilon ) dimensions, the flow diagram of the interactions and the critical exponents are investigated, within the two-loop approximation, in terms of the epsilon 1/2 expansion. It is shown that the transition that appears is a first-order transition.

Journal of Physics C Solid State PhysicsSep 10, 19856 citations

Critical exponents for cubic and impure uniaxial crystals: most accurate (?) theoretical values

I. O. Mayer, Aleksandr Ivanovich Sokolov, B. N. Shalaev

RG functions are calculated up to 4-loop order in 3 and 2 dimensions to evaluate, within Chisholm-Borel resummation technique, critical exponents for cubic and impure uniaxial crystals and the order parameter critical dimensionality nc . For 3D impure Ising crystals γ = 1.326, v = 0.670, α = -0.011, β = 0.342, η = 0.034, while critical exponents of 3D cubic crystals practically coincide with those of the Heisenberg model; nc = 2.9. For 2D systems the fermion representation enables us to find that their critical behavior is identical to that of pure Ising model, apart some logarithmic factors.RG functions are calculated up to 4-loop order in 3 and 2 dimensions to evaluate, within Chisholm-Borel resummation technique, critical exponents for cubic and impure uniaxial crystals and the order parameter critical dimensionality nc . For 3D impure Ising crystals γ = 1.326, v = 0.670, α = -0.011, β = 0.342, η = 0.034, while critical exponents of 3D cubic crystals practically coincide with those of the Heisenberg model; nc = 2.9. For 2D systems the fermion representation enables us to find that their critical behavior is identical to that of pure Ising model, apart some logarithmic factors.

FerroelectricsJul 1, 198969 citations

On the critical dynamics of extended-impurity systems in cubic anisotropic crystals

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