arXiv subjects

Jordi Comellas

Publications and source records attributed to Jordi Comellas.

7 recordsLinked to original sources

arXiv1997

O(N) models within the local potential approximation

Using Wegner-Houghton equation, within the Local Potential Approximation, we study critical properties of O(N) vector models. Fixed Points, together with their critical exponents and eigenoperators, are obtained for a large set of values of N, including N=0 and N\to\infty. Polchinski equation is also treated. The peculiarities of the large N limit, where a line of Fixed Points at d=2+2/n is present, are studied in detail. A derivation of the equation is presented together with its projection to zero modes.

hep-th↗

arXiv1997

Polchinski equation, reparameterization invariance and the derivative expansion

The connection between the anomalous dimension and some invariance properties of the fixed point actions within exact RG is explored. As an application, Polchinski equation at next-to-leading order in the derivative expansion is studied. For the Wilson fixed point of the one-component scalar theory in three dimensions we obtain the critical exponents η=0.042, ν=0.622 and ω=0.754.

hep-th↗

arXiv1997

Exact renormalization group study of fermionic theories

The exact renormalization group approach (ERG) is developed for the case of pure fermionic theories by deriving a Grassmann version of the ERG equation and applying it to the study of fixed point solutions and critical exponents of the two-dimensional chiral Gross-Neveu model. An approximation based on the derivative expansion and a further truncation in the number of fields is used. Two solutions are obtained analytically in the limit $N\to \infty $, with N being the number of fermionic species. For finite N some fixed point solutions, with their anomalous dimensions and critical exponents, are computed numerically. The issue of separation of physical results from the numerous spurious ones is discussed. We argue that one of the solutions we find can be identified with that of Dashen and Frishman, whereas the others seem to be new ones.

hep-th↗

arXiv1996

Exact Renormalization Group with Fermions

The development of the Exact Renormalization Group for fermionic theories is presented, together with its application to the chiral Gross-Neveu model. We focus on the reliability of various approximations, specifically the derivative expansion and further truncations in the number of fields. The main differences with bosonic theories are discussed.

hep-th↗

arXiv1996

Wilsonian vs. 1PI renormalization group flow irreversibility

We present a line of reasoning based on the analysis of scale variations of the Wilsonian partition function and the trace of the stress tensor in a curved manifold which results in a statement of irreversibility of Wilsonian renormalization group flow for unitary theories. We also analyze subtleties related to subtractions in the case of the 1PI effective action flow.

hep-th↗

arXiv1996

Approximate solutions in scalar and fermionic theories within the exact renormalization group approach

We give a review of the exact renormalization group (ERG) approach and illustrate its applications in scalar and fermionic theories. The derivative expansion and approximations based on the derivative expansion with further truncation in the number of fields (mixed approximation) are discussed. We analyse the mixed approximation for a three-dimensional scalar theory and show that it is less effective than the pure derivative expansion. For pure fermionic theories analytical solutions for the pure derivative expansion and mixed approximation in the limit $N \to \infty $, where $N$ is the number of fermionic species, are found. For finite $N$ a few series of fixed point solutions with their anomalous dimensions and critical exponents are computed numerically. We argue that one of the fermionic solutions can be identified with that of Dashen and Frishman, whereas the others seem to be new ones. The issues of spurious solutions and scheme dependence of the results are discussed.

hep-th↗

arXiv1995

Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities

We explore some of the constraints imposed by positivity of the QCD measure (Weingarten's inequalities) on the parameters defining chiral perturbation theory. We find, in particular, that $2 m_q (μ)\leq B_0(μ) Z(μ)$. The use of further properties of the exact fermion propagator yields information on some higher order parameters.

hep-ph↗