Set Of Critical Exponents Research Articles

Spin Anisotropy and Critical Exponents for a Heisenberg System A Renormalization Group Approach

AbstractFirstly the renormalization group technique is applied to an isotropic Heisenberg spin system with long‐range interaction and a set of critical exponents are calculated. These exponents are expressed in terms of a potential parameter s̀. All critical exponents except β, the magnetization exponent, depend on s̀. Secondly, the anisotropy is considered and the related crossover exponent φ is evaluated. This later parameter turns out to be equal to γ, the susceptibility exponent, as predicted by some authors.

Critical behavior of Fe 15Ni 65B 18Si 2 ferromagnetic glass

AC susceptibility, magnetization and electrical resistivity around the Curie temperature ( T c) were measured for Fe 15Ni 65B 18Si 2 glass. The results yield T c = (307.6±0.1) K and the following critical exponents γ = 1.50±0.03, β = 0.375±0.01, δ = 5.1±0.1 and α = -0.29±0.05. These values were obtained in the reduced temperature interval 1×10 -3 ⩽ |T−T c| T c ⪕5 ×10 -2 . In spite of the fact that these values for the critical exponents were obtained from different measurements they obey the equality relations γ = β( δ−1) and γ+2 β+ α = 2. Reduced magnetisation and field follow a magnetic equation of state derived for a second-order phase transition over a wide temperature range. This set of critical exponents is compared with those derived from the Heisenberg model as well as with the usual ones for a pure crystalline ferromagnets. The comparison shows that the values of |α| and γ, for our alloy, are considerably larger than those from the model and the usual crystalline ones. A similar difference is also observed in some other amorphous and dilute crystalline ferromagnets and is probably due to magnetic inhomogeneities.

Correlations in the face-centred cubic Ising model below Tcand along the critical isotherm

Correlations near the critical point of a face-centred cubic lattice are studied by series expansion methods. The amplitude of the second moment correlation length xi 1 is calculated for several sets of critical exponents.

Critical exponents for order-disorder phase transitions from second-harmonic scattering: two critical regions for NH4Cl

A method is presented for analysing second-harmonic scattering data which allows the determination of the set of critical exponents gamma , nu and eta for an order-disorder phase transition. Application to recent data for NH4Cl reveals the unsuspected existence of two distinct critical regions above Tc with a different set of critical exponents for each region. Moreover, each set of critical exponents differs greatly from the corresponding exponents for all known substances and for all theoretical models studied to date. The authors have no explanation for this anomaly.