Critical Exponent Eta Research Articles

Continuum-limit correlation functions for the spin-one anisotropic Heisenberg chain

The authors derive a continuum representation of the spin-one operators which provides the mapping of the spin-one anisotropic Heisenberg chain onto the Luttinger model. They show a schematic phase diagram of the Hamiltonian, and calculate a general two-spin dynamic correlation function at finite temperatures, valid in the massless domain of the Hamiltonian. This can be applied to obtain the transverse dynamic form factor, and results are compared with neutron scattering data on CsNiF3. The behaviour of the transverse correlation function is shown to be governed by a critical exponent eta u+or- which is a measured of quantum effects in the system, eta M+or- to 0 being the classical limit. Existing data on CsNiF3 are shown to be in the classical regime, and they make suggestions for further experiments to search for quantum fluctuations. They also indicate the limits of applicability of the quantum sine-Gordon theory to CsNIF3.

Renormalisation group calculations of the critical exponents of the n-vector model with a free surface

The correlation function critical exponents eta /sub /// and eta perpendicular to of the semi-infinite phi 4 model with O(n) symmetry have been calculated to order epsilon 2 for the ordinary and special transitions. The results for the ordinary transition are inconsistent with the relation gamma 11= nu -1 proposed by Bray and Moore (1977). Comparisons with series expansion results in two and three dimensions are presented for n=0 and n=1.

Non-universality for two-dimensional frustrated lattices?

An exact relationship between the eight vertex (8V) model and the fully frustrated square Ising model (FFSI) is established. On the basis of this it is shown that the T=0 point of the FFSI model corresponds to the F model limit of the 8V model. The critical exponent eta =1/4 for the FFSI model is obtained. The corresponding value of eta for the fully frustrated triangular lattice was shown by Stephenson (1964, 1966) to be 1/2. Possible reasons for this apparent violation of universality are discussed.

On the decay of anisotropy approaching the critical point

A recent investigation by Nattermann and Trimper, (see J. Phys. A., vol.8, p.200, 1975), of the influence of cubic anisotropy in both the quadratic and quartic parts of an n-component order parameter Hamiltonian is extended in order to examine the decay of the anisotropy near the critical point. In the case where the transition is driven to first order by the anisotropic fluctuations, the 'size' of the first-order transition is estimated. It turns out that this first-order transition becomes experimentally observable only for large values of the lattice anisotropy. The effective and asymptotic critical exponents eta and zeta (the latter characterizes the decay of the anisotropy) are calculated. The competition between the decay of the anisotropy and the occurrence of a first-order transition in investigated. The results give an explanation for the first-order transition in KMnF3. The extension of this approach to lower-than-cubic symmetry is briefly discussed.

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.