12,044 research outputs found
Precise determination of critical exponents and equation of state by field theory methods
Renormalization group, and in particular its Quantum Field Theory
implementation has provided us with essential tools for the description of the
phase transitions and critical phenomena beyond mean field theory. We therefore
review the methods, based on renormalized phi^4_3 quantum field theory and
renormalization group, which have led to a precise determination of critical
exponents of the N-vector model (R. Guida and J. Zinn-Justin, J. Phys. A31
(1998) 8103. cond-mat/9803240). and of the equation of state of the 3D Ising
model (R. Guida and J. Zinn-Justin, Nucl. Phys. B489 [FS] (1997) 626,
hep-th/9610223.). These results are among the most precise available probing
field theory in a non-perturbative regime.Comment: 23 pages, tex, private macros, one figur
High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture
A numerical method of high precision is used to calculate the energy
eigenvalues and eigenfunctions for a symmetric double-well potential. The
method is based on enclosing the system within two infinite walls with a large
but finite separation and developing a power series solution for the
Schrdinger equation. The obtained numerical results are compared with
those obtained on the basis of the Zinn-Justin conjecture and found to be in an
excellent agreement.Comment: Substantial changes including the title and the content of the paper
8 pages, 2 figures, 3 table
Apparently noninvariant terms of nonlinear sigma model in the one-loop approximation
We show how the Apparently Noninvariant Terms (ANTs), which emerge in
perturbation theory of nonlinear sigma models, are consistent with the
nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the
form of an inhomogeneous Zinn-Justin equation). In the literature the
discussions on ANTs are confined to the SU(2) case. We generalize them to the
U(N) case and demonstrate explicitly at the one-loop level that despite the
presence of divergent ANTs in the effective action of the "pions", the symmetry
is preserved.Comment: two paragraphs added in Introduction, typos in Eqs. fixe
Random vector and matrix and vector theories: a renormalization group approach
Random matrices in the large N expansion and the so-called double scaling
limit can be used as toy models for quantum gravity: 2D quantum gravity coupled
to conformal matter. This has generated a tremendous expansion of random matrix
theory, tackled with increasingly sophisticated mathematical methods and number
of matrix models have been solved exactly. However, the somewhat paradoxical
situation is that either models can be solved exactly or little can be said.
Since the solved models display critical points and universal properties, it is
tempting to use renormalization group ideas to determine universal properties,
without solving models explicitly. Initiated by Br\'ezin and Zinn-Justin, the
approach has led to encouraging results, first for matrix integrals and then
quantum mechanics with matrices, but has not yet become a universal tool as
initially hoped. In particular, general quantum field theories with matrix
fields require more detailed investigations. To better understand some of the
encountered difficulties, we first apply analogous ideas to the simpler O(N)
symmetric vector models, models that can be solved quite generally in the large
N limit. Unlike other attempts, our method is a close extension of Br\'ezin and
Zinn-Justin. Discussing vector and matrix models with similar approximation
scheme, we notice that in all cases (vector and matrix integrals, vector and
matrix path integrals in the local approximation), at leading order,
non-trivial fixed points satisfy the same universal algebraic equation, and
this is the main result of this work. However, its precise meaning and role
have still to be better understood
Lorentzian Wetterich equation for gauge theories
In a recent paper, with Drago and Pinamonti we have introduced a
Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using
the algebraic approach to perturbative QFT. The equation governs the flow of
the average effective action, under changes of a mass parameter k. Here we
introduce an analogous flow equation for gauge theories, with the aid of the
Batalin-Vilkovisky (BV) formalism. We also show that the corresponding average
effective action satisfies an extended Slavnov-Taylor identity in Zinn-Justin
form. We interpret the equation as a cohomological constraint on the functional
form of the average effective action, and we show that it is consistent with
the flow.Comment: 42 page
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