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Momentum-resolved direct and inverse photoemission spectra of the $\mathrm{K}/\mathrm{Si}\left(111\right)\ensuremath{-}(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}\mathrm{B}$ interface reveals the presence of strongly localized surface states. The K overlayer remains nonmetallic up to the saturation coverage. This system most likely presents the first experimental realization of a frustrated spin $1/2$ Heisenberg antiferromagnet on a two-dimensional triangular lattice.

High-temperature series for two bcc lattice models which interpolate between the Gaussian (or free-field) model and the $S=\frac{1}{2}$ Ising model are analyzed by partial differential approximants. Series to order 21 in both $x\ensuremath{\propto}\frac{1}{T}$ and the interpolation parameter, $y$, yield unbiased estimates for the correction-to-scaling exponent, $\ensuremath{\theta}=0.54\ifmmode\pm\else\textpm\fi{}5$, and the susceptibility exponent, $\ensuremath{\gamma}=1.2385\ifmmode\pm\else\textpm\fi{}15$. The results are universal and agree tolerably with field-theoretic estimates and well with biased, one-variable analyses of general spin Ising models.

Crossover near the fluctuation-induced first-order transition in superconductors is studied to first order in $\ensuremath{\epsilon}=4\ensuremath{-}d$. We find that the effective exponent ${\ensuremath{\gamma}}_{\mathrm{eff}}$ for the susceptibility of type-II systems falls from its value for the chargeless system to the mean-field value unity well before the first-order transition occurs. Although such effects are probably unobservable in real superconductors, these calculations may have some relevance to the nematic to smectic-$A$ transition in liquid crystals.

The exponents γ, ν and α are estimated from susceptibility and correlation length series for the bcc double-Gaussian and Klauder models, which interpolate, as a function of y, between the pure Gaussian model (at y=0) and the pure spin 1/2 Ising model (at y=1). Single-variable analysis reveals a value, y c (for each model), at which the leading, non-analytic corrections to pure power laws vanish, in accordance with expectations based on prior partial differential approximant analysis. The Hamiltonians of the two models display quasiuniversal features at these points. The corresponding exponent estimates are γ=1.2395±0.0004, ν=0.632±0.001 and α=0.105±0.007: these imply dν−(2−α)=0.001±0.010 and hence indicate the validity of hyperscaling. Apparent violations seen in the pure Ising model are attribuate to small but significant nonanalytic corrections Nous calculons les exposants γ, ν et α a partir des developpements en serie de la longueur de correlation et de la susceptibilite magnetique dans les modeles double gaussien et de Klauder sur reseaux cubiques centres. Ces modeles interpolent en fonction d'un parametre y entre le modele gaussien pur (y=0) et le modele d'Ising de spin 1/2 (y=1). Une analyse a une variable suggere l'existence d'une valeur y c (pour chaque modele) pour laquelle la premiere correction non analytique a une pure loi de puissance s'annule. Ce resultat est en accord avec une analyse anterieure utilisant des approximants differentiels a deux variables. Les hamiltoniens des deux modeles ont des caracteristiques quasi universelles en ces points. Nous en deduisons une estimation pour les exposants critiques: γ=1,2395±0,0004, ν=0,632±0,001, α=0,105±0,007: ceci implique dν−(2−α)=0,001±0,010 et indique que l'«hyperscaling» est verifie. Des deviations apparentes observees dans le modele d'Ising pur peuvent etre attribuees a des corrections non analytiques petites, mais non negligeables

Recent experiments on MnF2 (King and Rohrer, 1976, 1979) suggest Q=1.56+or-0.35 for the amplitude ratio determining how the critical lines meet at the spin-flop bicritical point, in serious disagreement with the original prediction of Q approximately=2.5>2.2 for universal Heisenberg (n=3) bicriticality. The authors report extensive two-variable series calculations using constrained partial differential approximants, which yield Q=2.34+or-0.08. In addition it is shown that the natural least-squares fitting procedures may be strongly biased even for data of high precision.

A Landau-Ginzburg free energy is presented that yields a nematic to smectic-$A$ (NA) transition, a nematic to smectic-$C$ (NC) transition, and a Lifshitz point (at the boundary between the NA and NC transitions). Fluctuation enhancements of the Frank elastic constants are calculated. For the NC transition, all three elastic constants ${K}_{1}$, ${K}_{2}$, and ${K}_{3}$ diverge as ${\ensuremath{\xi}}^{2}$, where $\ensuremath{\xi}$ is the correlation length for fluctuations of the smectic order parameter. At the Lifshitz point, ${K}_{1}$ and ${K}_{2}$ diverge as $\mathrm{ln}\ensuremath{\xi}$ whereas ${K}_{3}$ diverges as $\ensuremath{\xi}$.

The critical properties of the model of a spin-glass proposed by Edwards and Anderson are studied using the renormalization group. The critical exponents are calculated in $6\ensuremath{-}\ensuremath{\epsilon}$ spatial dimensions. It is argued that a tricritical point can exist where the nonordering field is the skewness of the distribution of $J$.