Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first one corresponds to $\Theta = T_S / T_M = \infty$ and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at $\Theta = 0$ and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.Comment: 18 pages, RevTeX, 1 figure included as eps-file; submitted to Phys. Rev.

Critical Behavior of the Supersolid transition in Bose-Hubbard Models

We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF--CSS transition is in the three-dimensional XY universality class. The SF--XSS transition exhibits non-trivial new critical behavior, and appears, within a $d=3-\epsilon$ expansion to be driven generically first order by fluctuations. However, within a one--loop calculation directly in $d=2$ a strong coupling fixed point with striking ``non-Bose liquid'' behavior is found. At special isolated multi-critical points of particle-hole symmetry, the system falls into the 3d Ising universality class.Comment: RevTeX, 24 pages, 16 figures. Also available at http://www.cip.physik.tu-muenchen.de/tumphy/d/T34/Mitarbeiter/frey.htm

Tetracritical behavior in strongly interacting theories

We suggest a tetracritical fixed point to naturally occur in strongly interacting theories. As a fundamental example we analyze the temperature--quark chemical potential phase diagram of QCD with fermions in the adjoint representation of the gauge group (i.e. adjoint QCD). Here we show that such a non trivial multicritical point exists and is due to the interplay between the spontaneous breaking of a global U(1) symmetry and the center group symmetry associated to confinement. Our results demonstrate that taking confinement into account is essential for understanding the critical behavior as well as the full structure of the phase diagram of adjoint QCD. This is in contrast to ordinary QCD where the center group symmetry associated to confinement is explicitly broken when the quarks are part of the theory.Comment: RevTex, 5 figures. Final version to appear in PR

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.