3,553 research outputs found
Analytic calculation of the 1-loop effective action for the O(N+1)-symmetric 2-dimensional nonlinear sigma-model
Polyakov's calculation of the effective action for the 2d nonlinear
sigma-Model is generalized by purely analytic means to include contributions
which are not UV-divergent and which depend on the choice of block spin. An
analytic approximation to the background field which determines the classical
perfect action is given, and approximations to the 1-loop correction are found.
The results should be useful for numerical simulations.Comment: 38 p, 1 figur
1-Loop improved lattice action for the nonlinear sigma-model
In this paper we show the Wilson effective action for the 2-dimensional
O(N+1)-symmetric lattice nonlinear sigma-model computed in the 1-loop
approximation for the nonlinear choice of blockspin , \Phi(x)=
\Cav\phi(x)/{|\Cav\phi(x)|},where \Cav is averaging of the fundamental field
over a square of side .
The result for is composed of the classical perfect action with a
renormalized coupling constant , an augmented contribution from a
Jacobian, and further genuine 1-loop correction terms. Our result extends
Polyakov's calculation which had furnished those contributions to the effective
action which are of order , where is the lattice spacing
of the fundamental lattice. An analytic approximation for the background field
which enters the classical perfect action will be presented elsewhere.Comment: 3 (2-column format) pages, 1 tex file heplat99.tex, 1 macro package
Espcrc2.sty To appear in Nucl. Phys. B, Proceedings Supplements Lattice 9
Clustering of fermionic truncated expectation values via functional integration
I give a simple proof that the correlation functions of many-fermion systems
have a convergent functional Grassmann integral representation, and use this
representation to show that the cumulants of fermionic quantum statistical
mechanics satisfy l^1-clustering estimates
Constructive Field Theory and Applications: Perspectives and Open Problems
In this paper we review many interesting open problems in mathematical
physics which may be attacked with the help of tools from constructive field
theory. They could give work for future mathematical physicists trained with
the constructive methods well within the 21st century
Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials
We show how to compute real space renormalization group flows in lattice
field theory by a self-consistent method. In each step, the integration over
the fluctuation field (high frequency components of the field) is performed by
a saddle point method. The saddle point depends on the block-spin. Higher
powers of derivatives of the field are neglected in the actions, but no
polynomial approximation in the field is made. The flow preserves a simple
parameterization of the action. In this paper we treat scalar field theories as
an example.Comment: 52 pages, uses pstricks macro, three ps-figure
The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3
We consider an Euclidean supersymmetric field theory in given by a
supersymmetric perturbation of an underlying massless Gaussian measure
on scalar bosonic and Grassmann fields with covariance the Green's function of
a (stable) L\'evy random walk in . The Green's function depends on the
L\'evy-Khintchine parameter with . For
the interaction is marginal. We prove for
sufficiently small and initial
parameters held in an appropriate domain the existence of a global
renormalization group trajectory uniformly bounded on all renormalization group
scales and therefore on lattices which become arbitrarily fine. At the same
time we establish the existence of the critical (stable) manifold. The
interactions are uniformly bounded away from zero on all scales and therefore
we are constructing a non-Gaussian supersymmetric field theory on all scales.
The interest of this theory comes from the easily established fact that the
Green's function of a (weakly) self-avoiding L\'evy walk in is a second
moment (two point correlation function) of the supersymmetric measure governing
this model. The control of the renormalization group trajectory is a
preparation for the study of the asymptotics of this Green's function. The
rigorous control of the critical renormalization group trajectory is a
preparation for the study of the critical exponents of the (weakly)
self-avoiding L\'evy walk in .Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition
of norms involving fermions to ensure uniqueness. 2. change in the definition
of lattice blocks and lattice polymer activities. 3. Some proofs have been
reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos
corrected.This is the version to appear in Journal of Statistical Physic
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