25 research outputs found
Yang-Lee zeros of the Q-state Potts model in the complex magnetic-field plane
The microcanonical transfer matrix is used to study the distribution of
Yang-Lee zeros of the -state Potts model in the complex magnetic-field
() plane for the first time. Finite size scaling suggests that
at (and below) the critical temperature the zeros lie close to, but not on, the
unit circle with the two exceptions of the critical point () itself
and the zeros in the limit T=0.Comment: REVTeX, 12 pages, 5 figures, to appear in Phys. Rev. Let
Microcanonical Transfer Matrix Study of the Q-state Potts Model
The microcanonical transfer matrix is used to study the zeros of the
partition function of the Q-state Potts model. Results are presented for the
Yang-Lee zeros of the 3-state model, the Fisher zeros of the 3-state model in
an external field , and the spontaneous magnetization of the 2-state
model. In addition, we are able to calculate the ground-state entropy of the
3-state model and find in excellent agreement with the exact
value, 0.43152...Comment: 3 pages, 3 figures, LaTeX, to appear in Computer Physics
Communication
Renormalization group theory of the critical properties of the interacting bose fluid
Starting from a functional integral representation of the partition function we apply the renormalization group to the interacting Bose fluid. A closed form for the renormalization equation is derived and the critical exponents are calculated in 4-ε dimensions
Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier
The motion in the plane of an harmonically bound charged particle interacting with a magnetic field and a half-plane barrier along the positive x-axis is studied. The magnetic field is perpendicular to the plane in which the particle moves. This motion is integrable in between collisions of the particle with the barrier. However, the overall motion of the particle is very complicated. Chaotic regions in phase space exist next to island structures associated with linearly stable periodic orbits. We study in detail periodic orbits of low period and in particular their bifurcation behavior. Independent sequences of period doubling bifurcations and resonant bifurcations are observed associated with independent fixed points in the Poincaré section. Due to the perpendicular magnetic field an orientation is induced on the plane and time-reversal symmetry is broken.\u
Exact results for the zeros of the partition function of the Potts model on finite lattices
The Yang-Lee zeros of the Q-state Potts model are investigated in 1, 2 and 3
dimensions. Analytical results derived from the transfer matrix for the
one-dimensional model reveal a systematic behavior of the locus of zeros as a
function of Q. For 1<Q<2 the zeros in the complex plane lie
inside the unit circle, while for Q>2 they lie outside the unit circle for
finite temperature. In the special case Q=2 the zeros lie exactly on the unit
circle as proved by Lee and Yang. In two and three dimensions the zeros are
calculated numerically and behave in the same way. Results are also presented
for the critical line of the Potts model in an external field as determined
from the zeros of the partition function in the complex temperature plane.Comment: 15 pages, 6 figures, RevTe
Partition function zeros of the Q-state Potts model for non-integer Q
The distribution of the zeros of the partition function in the complex
temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is
studied for non-integer Q. On self-dual lattices studied (),
no Fisher zero lies on the unit circle in the complex
plane for Q<1, while some of the Fisher zeros lie
on the unit circle for Q>1 and the number of such zeros increases with
increasing Q. The ferromagnetic and antiferromagnetic properties of the Potts
model are investigated using the distribution of the Fisher zeros. For the
Potts ferromagnet we verify the den Nijs formula for the thermal exponent
. For the Potts antiferromagnet we also verify the Baxter conjecture for
the critical temperature and present new results for the thermal exponents in
the range 0<Q<3.Comment: 12 pages, 7 figures, RevTe