597 research outputs found
Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model
The scaling behaviour of the edge of the Lee--Yang zeroes in the four
dimensional Ising model is analyzed. This model is believed to belong to the
same universality class as the model which plays a central role in
relativistic quantum field theory. While in the thermodynamic limit the scaling
of the Yang--Lee edge is not modified by multiplicative logarithmic
corrections, such corrections are manifest in the corresponding finite--size
formulae. The asymptotic form for the density of zeroes which recovers the
scaling behaviour of the susceptibility and the specific heat in the
thermodynamic limit is found to exhibit logarithmic corrections too. The
density of zeroes for a finite--size system is examined both analytically and
numerically.Comment: 17 pages (4 figures), LaTeX + POSTSCRIPT-file, preprint UNIGRAZ-UTP
20-11-9
The Phases and Triviality of Scalar Quantum Electrodynamics
The phase diagram and critical behavior of scalar quantum electrodynamics are
investigated using lattice gauge theory techniques. The lattice action fixes
the length of the scalar (``Higgs'') field and treats the gauge field as
non-compact. The phase diagram is two dimensional. No fine tuning or
extrapolations are needed to study the theory's critical behovior. Two lines of
second order phase transitions are discovered and the scaling laws for each are
studied by finite size scaling methods on lattices ranging from through
. One line corresponds to monopole percolation and the other to a
transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent
specific heats. The lines of transitions cross in the interior of the phase
diagram and appear to be unrelated. The monopole percolation transition has
critical indices which are compatible with ordinary four dimensional
percolation uneffected by interactions. Finite size scaling and histogram
methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line
are well-fit by the hypothesis that scalar quantum electrodynamics is
logarithmically trivial. The logarithms are measured in both finite size
scaling of the specific heat peaks as a function of volume as well as in the
coupling constant dependence of the specific heats measured on fixed but large
lattices. The theory is seen to be qualitatively similar to .
The standard CRAY random number generator RANF proved to be inadequateComment: 25pages,26figures;revtex;ILL-(TH)-94-#12; only hardcopy of figures
availabl
The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for
nonequilibrium dynamics, in particular driven diffusive processes. It is
usually considered in a canonical ensemble in which the number of sites is
fixed. We observe that the grand-canonical partition function for the ASEP is
remarkably simple. It allows a simple direct derivation of the asymptotics of
the canonical normalization in various phases and of the correspondence with
One-Transit Walks recently observed by Brak et.al.Comment: Published versio
Quasi-long-range ordering in a finite-size 2D Heisenberg model
We analyse the low-temperature behaviour of the Heisenberg model on a
two-dimensional lattice of finite size. Presence of a residual magnetisation in
a finite-size system enables us to use the spin wave approximation, which is
known to give reliable results for the XY model at low temperatures T. For the
system considered, we find that the spin-spin correlation function decays as
1/r^eta(T) for large separations r bringing about presence of a
quasi-long-range ordering. We give analytic estimates for the exponent eta(T)
in different regimes and support our findings by Monte Carlo simulations of the
model on lattices of different sizes at different temperatures.Comment: 9 pages, 3 postscript figs, style files include
Ising spins coupled to a four-dimensional discrete Regge skeleton
Regge calculus is a powerful method to approximate a continuous manifold by a
simplicial lattice, keeping the connectivities of the underlying lattice fixed
and taking the edge lengths as degrees of freedom. The discrete Regge model
employed in this work limits the choice of the link lengths to a finite number.
To get more precise insight into the behavior of the four-dimensional discrete
Regge model, we coupled spins to the fluctuating manifolds. We examined the
phase transition of the spin system and the associated critical exponents. The
results are obtained from finite-size scaling analyses of Monte Carlo
simulations. We find consistency with the mean-field theory of the Ising model
on a static four-dimensional lattice.Comment: 19 pages, 7 figure
Fisher Zeroes and Singular Behaviour of the Two Dimensional Potts Model in the Thermodynamic Limit
The duality transformation is applied to the Fisher zeroes near the
ferromagnetic critical point in the q>4 state two dimensional Potts model. A
requirement that the locus of the duals of the zeroes be identical to the dual
of the locus of zeroes in the thermodynamic limit (i) recovers the ratio of
specific heat to internal energy discontinuity at criticality and the
relationships between the discontinuities of higher cumulants and (ii)
identifies duality with complex conjugation. Conjecturing that all zeroes
governing ferromagnetic singular behaviour satisfy the latter requirement gives
the full locus of such Fisher zeroes to be a circle. This locus, together with
the density of zeroes is then shown to be sufficient to recover the singular
form of the thermodynamic functions in the thermodynamic limit.Comment: 10 pages, 0 figures, LaTeX. Paper expanded and 2 references added
clarifying duality relationships between discontinuities in higher cumulant
Classical phase transitions in a one-dimensional short-range spin model
Ising's solution of a classical spin model famously demonstrated the absence
of a positive-temperature phase transition in one-dimensional equilibrium
systems with short-range interactions. No-go arguments established that the
energy cost to insert domain walls in such systems is outweighed by entropy
excess so that symmetry cannot be spontaneously broken. An archetypal way
around the no-go theorems is to augment interaction energy by increasing the
range of interaction. Here we introduce new ways around the no-go theorems by
investigating entropy depletion instead. We implement this for the Potts model
with invisible states.Because spins in such a state do not interact with their
surroundings, they contribute to the entropy but not the interaction energy of
the system. Reducing the number of invisible states to a negative value
decreases the entropy by an amount sufficient to induce a positive-temperature
classical phase transition. This approach is complementary to the long-range
interaction mechanism. Alternatively, subjecting positive numbers of invisible
states to imaginary or complex fields can trigger such a phase transition. We
also discuss potential physical realisability of such systems.Comment: 29 pages, 11 figure
Four-dimensional pure compact U(1) gauge theory on a spherical lattice
We investigate the confinement-Coulomb phase transition in the
four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The
action contains the Wilson coupling beta and the double charge coupling gamma.
The lattice is obtained from the 4D surface of the 5D cubic lattice by its
radial projection onto a 4D sphere, and made homogeneous by means of
appropriate weight factors for individual plaquette contributions to the
action. On such lattices the two-state signal, impeding the studies of this
theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a
consistent finite-size scaling behavior of several bulk observables is found,
with the correlation length exponent nu in the range nu = 0.35 - 40. These
observables include Fisher zeros, specific-heat and cumulant extrema as well as
pseudocritical values of beta at fixed gamma. The most reliable determination
of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at
gamma le 0 is thus very probably of 2nd order and belongs to the universality
class of a non-Gaussian fixed point.Comment: 40 pages, LaTeX, 12 figure
Dynamical fermion mass generation at a tricritical point in strongly coupled U(1) lattice gauge theory
Fermion mass generation in the strongly coupled U(1) lattice gauge theory
with fermion and scalar fields of equal charge is investigated by means of
numerical simulation with dynamical fermions. Chiral symmetry of this model is
broken by the gauge interaction and restored by the light scalar. We present
evidence for the existence of a particular, tricritical point of the
corresponding phase boundary where the continuum limit might possibly be
constructed. It is of interest as a model for dynamical symmetry breaking and
mass generation due to a strong gauge interaction. In addition to the massive
and unconfined fermion F and Goldstone boson , a gauge ball of mass and some other states are found. Tricritical exponents appear
to be non-classical.Comment: 21 page
Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q
The Q-state Potts model can be extended to noninteger and even complex Q in
the FK representation. In the FK representation the partition function,Z(Q,a),
is a polynomial in Q and v=a-1(a=e^-T) and the coefficients of this
polynomial,Phi(b,c), are the number of graphs on the lattice consisting of b
bonds and c connected clusters. We introduce the random-cluster transfer matrix
to compute Phi exactly on finite square lattices. Given the FK representation
of the partition function we begin by studying the critical Potts model
Z_{CP}=Z(Q,a_c), where a_c=1+sqrt{Q}. We find a set of zeros in the complex
w=sqrt{Q} plane that map to the Beraha numbers for real positive Q. We also
identify tilde{Q}_c(L), the value of Q for a lattice of width L above which the
locus of zeros in the complex p=v/sqrt{Q} plane lies on the unit circle. We
find that 1/tilde{Q}_c->0 as 1/L->0. We then study zeros of the AF Potts model
in the complex Q plane and determine Q_c(a), the largest value of Q for a fixed
value of a below which there is AF order. We find excellent agreement with
Q_c=(1-a)(a+3). We also investigate the locus of zeros of the FM Potts model in
the complex Q plane and confirm that Q_c=(a-1)^2. We show that the edge
singularity in the complex Q plane approaches Q_c as Q_c(L)~Q_c+AL^-y_q, and
determine the scaling exponent y_q. Finally, by finite size scaling of the
Fisher zeros near the AF critical point we determine the thermal exponent y_t
as a function of Q in the range 2<Q<3. We find that y_t is a smooth function of
Q and is well fit by y_t=(1+Au+Bu^2)/(C+Du) where u=u(Q). For Q=3 we find
y_t~0.6; however if we include lattices up to L=12 we find y_t~0.50.Comment: to appear in Physical Review
- …