1,049 research outputs found
Logarithmic Corrections to Scaling in the --Model
We study the distribution of partition function zeroes for the --model in
two dimensions. In particular we find the scaling behaviour of the end of the
distribution of zeroes in the complex external magnetic field plane in the
thermodynamic limit (the Yang--Lee edge) and the form for the density of these
zeroes. Assuming that finite--size scaling holds, we show that there have to
exist logarithmic corrections to the leading scaling behaviour of thermodynamic
quantities in this model. These logarithmic corrections are also manifest in
the finite--size scaling formulae and we identify them numerically. The method
presented here can be used to check the compatibility of scaling behaviour of
odd and even thermodynamic functions in other models too.Comment: 3 pages, latex, 2 figure
Universal Amplitude Ratios for Constrained Critical Systems
The critical properties of systems under constraint differ from their ideal
counterparts through Fisher renormalization. The mathematical properties of
Fisher renormalization applied to critical exponents are well known: the
renormalized indices obey the same scaling relations as the ideal ones and the
transformations are involutions in the sense that re-renormalizing the critical
exponents of the constrained system delivers their original, ideal
counterparts. Here we examine Fisher renormalization of critical amplitudes and
show that, unlike for critical exponents, the associated transformations are
not involutions. However, for ratios and combinations of amplitudes which are
universal, Fisher renormalization is involutory.Comment: JSTAT published versio
Critical Behaviour of the Two Dimensional Step Model
We use finite--size scaling of Lee--Yang partition function zeroes to study
the critical behaviour of the two dimensional step or sgn model. We
present evidence that, like the closely related --model, this has a phase
transition from a disordered high temperature phase to a low temperature
massless phase where the model remains critical. The critical parameters
(including logarithmic corrections) are compatible with those of the
--model indicating that both models belong to the same universality class.Comment: 6 pages latex, 3 postscript figures, compressed and uuencoded
(revised remarks on Lee_Yang theorem, version to appear in Phys Rev B
Phase Transition Strength through Densities of General Distributions of Zeroes
A recently developed technique for the determination of the density of
partition function zeroes using data coming from finite-size systems is
extended to deal with cases where the zeroes are not restricted to a curve in
the complex plane and/or come in degenerate sets. The efficacy of the approach
is demonstrated by application to a number of models for which these features
are manifest and the zeroes are readily calculable.Comment: 16 pages, 12 figure
Logarithmic Corrections to Scaling in the Two Dimensional --Model
By expressing thermodynamic functions in terms of the edge and density of
Lee--Yang zeroes, we relate the scaling behaviour of the specific heat to that
of the zero field magnetic susceptibility in the thermodynamic limit of the
--model in two dimensions. Assuming that finite--size scaling holds, we
show that the conventional Kosterlitz--Thouless scaling predictions for these
thermodynamic functions are not mutually compatable unless they are modified by
multiplicative logarithmic corrections. We identify these logarithmic
corrections analytically in the case of the specific heat and numerically in
the case of the susceptibility. The techniques presented here are general and
can be used to check the compatibility of scaling behaviour of odd and even
thermodynamic functions in other models too.Comment: 11 pages, latex, 4 figure
Role of topological defects in the phase transition of modified XY model : A Monte Carlo study
Monte Carlo simulation has been performed on a classical two dimensional XY-
model with a modified form of interaction potential to investigate the role of
topological defects on the phase transition exhibited by the model. In
simulations in a restricted ensemble without defects, the system appears to
remain ordered at all temperatures. Suppression of topological defects on the
square plaquettes in the modified XY- model leads to complete elimination of
the phase transition observed in this model.Comment: 19 pages, 12 figures, Accepted for publication in Phys. Rev.
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.
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