Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model

We introduce and study the properties of a periodic model interpolating between the sine-- and the sinh--Gordon theories in $1+1$ dimensions. This model shows the peculiarities, due to the preservation of the functional form of their potential across RG flows, of the two limiting cases: the sine-Gordon, not having conventional order/magnetization at finite temperature, but exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the sinh-Gordon, not having a phase transition, but being integrable. The considered interpolation, which we term as {\em sn-Gordon} model, is performed with potentials written in terms of Jacobi functions. The critical properties of the sn-Gordon theory are discussed by a renormalization-group approach. The critical points, except the sinh-Gordon one, are found to be of BKT type. Explicit expressions for the critical coupling as a function of the elliptic modulus are given.Comment: v2, 10 pages, 8 figures, accepted in J. Phys.

Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking

We study the occurrence of spontaneous symmetry breaking (SSB) for O (N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N = 1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions

HYPOGLYCEMIA ACTIVATES COMPENSATORY MECHANISM OF GLUCOSE METABOLISM OF BRAIN

The effect of plasma glucose concentration on the cerebral uptake of [18 F]-fluorodeoxy-D-glucose (FDG) was studied in a broad concentration range in a rabbit brain model using dynamic FDG PET measure- ments. Hypoglycemic and hyperglycemic conditions were maintained by manipulating plasma glucose applying i.v. glucose or insulin load. FDG utilization (K) and cerebral glucose metabolic rate (CGMR) were evaluated in a plasma glucose concentration range between 0.5 mM and 26 mM from the kinetic constant k1, k2, k3 obtained by the Sokoloff model of FDG accumulation. A decreasing set of standard FDG uptake values found with increasing blood glucose concentration was explained by competition between the plasma glucose and the radiopharmacon FDG. A similar trend was observed for the forward kinetic constants k1, and k3 in the entire concentration range studied. The same decreasing tendency of k2 was of a smaller magnitude and was reverted at the lowest glucose concentrations where a pronounced decrease of this backward transport rate constant was detected. Our kinetic data indicate a modulation of the kinetics of carbohydrate metabolism by the blood glucose concentration and report on a special mechanism compensating for the low glucose supply under conditions of extremely low blood glucose level

Vacuum Energy and Renormalization of the Field-Independent Term

Due to its Construction, the Nonperturbative Renormalization Group (RG) Evolution of the Constant, Field-Independent Term (Which is Constant with Respect to Field Variations But Depends on the RG Scale K) Requires Special Care within the Functional Renormalization Group (FRG) Approach. in Several Instances, the Constant Term of the Potential Has No Physical Meaning. However, There Are Special Cases Where It Receives Important Applications. in Low Dimensions (D = 1), in a Quantum Mechanical Model, This Term is Associated with the Ground-State Energy of the Anharmonic Oscillator. in Higher Dimensions (D = 4), It is Identical to the Λ Term of the Einstein Equations and It Plays a Role in Cosmic Inflation. Thus, in Statistical Field Theory, in Flat Space, the Constant Term Could Be Associated with the Free Energy, While in Curved Space, It Could Be Naturally Associated with the Cosmological Constant. It is Known that One Has to Use a Subtraction Method for the Quantum Anharmonic Oscillator in D = 1 to Remove the K 2 Term that Appears in the RG Flow in its High-Energy (UV) Limit in Order to Recover the Correct Results for the Ground-State Energy. the Subtraction is Needed Because the Gaussian Fixed Point is Missing in the RG Flow Once the Constant Term is Included. However, If the Gaussian Fixed Point is There, No Further Subtraction is Required. Here, We Propose a Subtraction Method for K 4 and K 2 Terms of the UV Scaling of the RG Equations for D = 4 Dimensions If the Gaussian Fixed Point is Missing in the RG Flow with the Constant Term. Finally, Comments on the Application of Our Results to Cosmological Models Are Provided