24,815 research outputs found
The Phase Structure of the Weakly Coupled Lattice Schwinger Model
The weak coupling expansion is applied to the single flavour Schwinger model
with Wilson fermions on a symmetric toroidal lattice of finite extent. We
develop a new analytic method which permits the expression of the partition
function as a product of pure gauge expectation values whose zeroes are the
Lee-Yang zeroes of the model. Application of standard finite-size scaling
techniques to these zeroes recovers previous numerical results for the small
and moderate lattice sizes to which those studies were restricted. Our
techniques, employable for arbitrarily large lattices, reveal the absence of
accumulation of these zeroes on the real hopping parameter axis at constant
weak gauge coupling. The consequence of this previously unobserved behaviour is
the absence of a zero fermion mass phase transition in the Schwinger model with
single flavour Wilson fermions at constant weak gauge coupling.Comment: 8 pages, 2 figures, insert to figure 2 include
The Structure of the Aoki Phase at Weak Coupling
A new method to determine the phase diagram of certain lattice fermionic
field theories in the weakly coupled regime is presented. This method involves
a new type of weak coupling expansion which is multiplicative rather than
additive in nature and allows perturbative calculation of partition function
zeroes. Application of the method to the single flavour Gross-Neveu model gives
a phase diagram consistent with the parity symmetry breaking scenario of Aoki
and provides new quantitative information on the width of the Aoki phase in the
weakly coupled sector.Comment: 9 pages, 1 figure (minor changes) To be published in Phys. Lett.
The Redner - Ben-Avraham - Kahng cluster system
We consider a coagulation model first introduced by Redner, Ben-Avraham and
Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J.
Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that
the reaction between a j-cluster and a k-cluster results in the creation of a
|j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this
paper we prove existence and uniqueness of solutions under reasonably general
conditions on the coagulation coefficients, and we also establish
differenciability properties and continuous dependence of solutions. Some
interesting invariance properties are also proved. Finally, we study the
long-time behaviour of solutions, and also present a preliminary analysis of
their scaling behaviour.Comment: 24 pages. 2 figures. Dedicated to Carlos Rocha and Luis Magalhaes on
the occasion of their sixtieth birthday
The Redner - Ben-Avraham - Kahng coagulation system with constant coefficients: the finite dimensional case
We study the behaviour as of solutions to the
Redner--Ben-Avraham--Kahng coagulation system with positive and compactly
supported initial data, rigorously proving and slightly extending results
originally established in [4] by means of formal arguments.Comment: 13 pages, 1 figur
Towards gauge theories in four dimensions
The abundance of infrared singularities in gauge theories due to unresolved
emission of massless particles (soft and collinear) represents the main
difficulty in perturbative calculations. They are typically regularized in
dimensional regularization, and their subtraction is usually achieved
independently for virtual and real corrections. In this paper, we introduce a
new method based on the loop-tree duality (LTD) theorem to accomplish the
summation over degenerate infrared states directly at the integrand level such
that the cancellation of the infrared divergences is achieved simultaneously,
and apply it to reference examples as a proof of concept. Ultraviolet
divergences, which are the consequence of the point-like nature of the theory,
are also reinterpreted physically in this framework. The proposed method opens
the intriguing possibility of carrying out purely four-dimensional
implementations of higher-order perturbative calculations at next-to-leading
order (NLO) and beyond free of soft and final-state collinear subtractions.Comment: Final version to appear in JHE
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