183 research outputs found
Finite size effects at phase transition in compact U(1) gauge theory
We present and discuss the results of a Monte-Carlo simulation of the phase
transition in pure compact U(1) lattice gauge theory with Wilson action on a
hypercubic lattice with periodic boundary conditions. The statistics are large
enough to make a thorough analysis of the size dependence of the gap. In
particular we find a non-zero latent heat in the infinite volume limit. We also
find that the critical exponents and are consistent with the
hyperscaling relation but confirm that the critical behavior is different from
a conventional first-order transition.Comment: Talk presented at Lattice '97; 3 pages, Latex fil
Scaling of magnetic monopoles in the pure compact QED
In the pure U(1) lattice gauge theory with the Villain action we find that
the monopole mass in the Coulomb phase and the monopole condensate in the
confinement phase scale according to simple power laws. This holds outside the
coupling region in which on finite toroidal lattices the metastability
phenomena occur. A natural explanation of the observed accuracy of the scaling
behaviour would be the second order of the phase transition between both phases
in the general space of couplings not far away from the Villain action.Comment: LATTICE99(Topology and Confinement) - 3 pages, 4 fig
Scaling of gauge balls and static potential in the confinement phase of the pure U(1) lattice gauge theory
We investigate the scaling behaviour of gauge-ball masses and static
potential in the pure U(1) lattice gauge theory on toroidal lattices. An
extended gauge field action is used with and -0.5. Gauge-ball correlation
functions with all possible lattice quantum numbers are calculated. Most
gauge-ball masses scale with the non-Gaussian exponent .
The gauge-ball mass scales with the Gaussian value in the investigated range of correlation lengths. The static potential is
examined with Sommer's method. The long range part scales consistently with
but the short range part tends to yield smaller values of . The
-function, having a UV stable zero, is obtained from the running
coupling. These results hold for both values, supporting universality.
Consequences for the continuum limit of the theory are discussed.Comment: Contribution to the Lattice 97 proceedings, LaTeX, 3 pages, 3 figure
Finite Size Analysis of the U(1) Background Field Effective Action
We apply the finite size scaling analysis to the derivative of the density of
the effective action for the lattice U(1) pure gauge theory in an external
constant magnetic field. We found the presence of a continuous phase
transition. Moreover, our extimate of of the critical parameters gives values
consistent with those extracted from the analysis of the specific heat.Comment: LaTeX2e, 12 pages (5 figures
Study of the order of the phase transition in pure U(1) gauge theory with Villain action
We address the question of the order of the deconfinement phase transition of
four dimensional U(1) lattice gauge theory. Simulations of the Z-gauge theory
dual to the Villain action on toroidal lattices up to lattice sizes of 28^4
give results consistent with both, a vanishing and a nonvanishing discontinuity
in the thermodynamic limit. A decision on the order of the phase transition
requires still larger lattice sizes.Comment: LATTICE98(gauge), 3 pages, 2 figure
U(1) Gauge Theory with Villain Action on Spherical Lattices
We have studied the U(1) gauge field theory with Villain (periodic Gaussian)
action on spherelike lattices. The effective size of the systems studied ranges
from 6 to 16. We do not observe any 2-state signal in the distribution function
of the plaquette expectation value at the deconfining phase transition. The
observed finite-size scaling behavior is consistent with a second order phase
transition. The obtained value of the critical exponent is nu =0.366(12) and
thus neither Gaussian (nu = 0.5) nor discontinuous (nu=0.25) type, indicating a
nontrivial continuum limit.Comment: 10 pages, LaTeX, 2 figure
Tricritical point in strongly coupled U(1) gauge theory with fermions and scalars
We investigate the tricritical point in the lattice fermion--gauge--scalar
model with U(1) gauge symmetry. In the vicinity of this point, in the phase
with the broken chiral symmetry, we observe the scaling behavior of the chiral
condensate and of the masses of composite fermion and composite scalar,
indicating the existence of an interesting continuum limit of the model at this
point.Comment: Contribution to Lattice 95, LaTeX file (4 pages), 5 ps-figures
appended (uuencoded
Spin and Gauge Systems on Spherical Lattices
We present results for 2D and 4D systems on lattices with topology homotopic
to the surface of a (hyper) sphere or . Finite size scaling is
studied in situations with phase transitions of first and second order type.
The Ising and Potts models exhibit the expected behaviour; for the 4D pure
gauge theory we find consistent scaling indicative of a second order
phase transition with critical exponent .Comment: 4 pages, LaTeX, 3 POSTSCRIPT figures (uuencoded
Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory
We investigate the continuum limit of the gauge-ball spectrum in the
four-dimensional pure U(1) lattice gauge theory. In the confinement phase we
identify various states scaling with the correlation length exponent . The square root of the string tension also scales with this
exponent, which agrees with the non-Gaussian fixed point exponent recently
found in the finite size studies of this theory. Possible scenarios for
constructing a non-Gaussian continuum theory with the observed gauge-ball
spectrum are discussed. The state, however, scales with a Gaussian
value . This suggests the existence of a second, Gaussian
continuum limit in the confinement phase and also the presence of a light or
possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb
phase we find evidence for a few gauge-balls, being resonances in multi-photon
channels; they seem to approach the continuum limit with as yet unknown
critical exponents. The maximal value of the renormalized coupling in this
phase is determined and its universality confirmed.Comment: 46 pages, 12 figure
Magnetic and chiral universality classes in a 3D Yukawa model
The 3D Yukawa model with U(1) chiral symmetry is investigated in a broad
interval of parameters using the Binder method. Critical exponents of the
Wilson-Fisher (magnetic) and Gross-Neveu (chiral) universality classes are
measured. The model is dominated by the chiral universality class. However at
weak coupling we observe a crossover between both classes, manifested by
difficulties with the Binder method which otherwise works well.Comment: 4 pages, contribution to LATTICE 9
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