Duality symmetry, strong coupling expansion and universal critical amplitudes in two-dimensional \Phi^{4} field models

We show that the exact beta-function \beta(g) in the continuous 2D g\Phi^{4} model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation \tilde{g}=d(g) such that \beta(d(g))=d'(g)\beta(g) is constructed and the approximate values of g^{*} computed from the duality equation d(g^{*})=g^{*} are shown to agree with the available numerical results. The calculation of the beta-function \beta(g) for the 2D scalar g\Phi^{4} field theory based on the strong coupling expansion is developed and the expansion of \beta(g) in powers of g^{-1} is obtained up to order g^{-8}. The numerical values calculated for the renormalized coupling constant g_{+}^{*} are in reasonable good agreement with the best modern estimates recently obtained from the high-temperature series expansion and with those known from the perturbative four-loop renormalization-group calculations. The application of Cardy's theorem for calculating the renormalized isothermal coupling constant g_{c} of the 2D Ising model and the related universal critical amplitudes is also discussed.Comment: 16 pages, REVTeX, to be published in J.Phys.A:Math.Ge

Critical behavior of weakly-disordered anisotropic systems in two dimensions

The critical behavior of two-dimensional (2D) anisotropic systems with weak quenched disorder described by the so-called generalized Ashkin-Teller model (GATM) is studied. In the critical region this model is shown to be described by a multifermion field theory similar to the Gross-Neveu model with a few independent quartic coupling constants. Renormalization group calculations are used to obtain the temperature dependence near the critical point of some thermodynamic quantities and the large distance behavior of the two-spin correlation function. The equation of state at criticality is also obtained in this framework. We find that random models described by the GATM belong to the same universality class as that of the two-dimensional Ising model. The critical exponent $\nu$ of the correlation length for the 3- and 4-state random-bond Potts models is also calculated in a 3-loop approximation. We show that this exponent is given by an apparently convergent series in $\epsilon=c-\frac{1}{2}$ (with $c$ the central charge of the Potts model) and that the numerical values of $\nu$ are very close to that of the 2D Ising model. This work therefore supports the conjecture (valid only approximately for the 3- and 4-state Potts models) of a superuniversality for the 2D disordered models with discrete symmetries.Comment: REVTeX, 24 pages, to appear in Phys.Rev.

Low-temperature renormalization group study of uniformly frustrated models for type-II superconductors

We study phase transitions in uniformly frustrated SU(N)-symmetric $(2+\epsilon)$-dimensional lattice models describing type-II superconductors near the upper critical magnetic field $H_{c2}(T)$. The low-temperature renormalization-group approach is employed for calculating the beta-function $\beta(T,f)$ with $f$ an arbitrary rational magnetic frustration. The phase-boundary line $H_{c2}(T)$ is the ultraviolet-stable fixed point found from the equation $\beta(T,f)=0$, the corresponding critical exponents being identical to those of the non-frustrated continuum system. The critical properties of the SU(N)-symmetric complex Ginzburg-Landau (GL) model are then examined in $(4+\epsilon)$ dimensions. The possibility of a continuous phase transition into the mixed state in such a model is suggested.Comment: REVTeX, 12 pages, to appear in the Phys.Rev.