19 research outputs found
Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries
An intrinsic curvature model is investigated using the canonical Monte Carlo
simulations on dynamically triangulated spherical surfaces of size upto N=4842
with two fixed-vertices separated by the distance 2L. We found a first-order
transition at finite curvature coefficient \alpha, and moreover that the order
of the transition remains unchanged even when L is enlarged such that the
surfaces become sufficiently oblong. This is in sharp contrast to the known
results of the same model on tethered surfaces, where the transition weakens to
a second-order one as L is increased. The phase transition of the model in this
paper separates the smooth phase from the crumpled phase. The surfaces become
string-like between two point-boundaries in the crumpled phase. On the
contrary, we can see a spherical lump on the oblong surfaces in the smooth
phase. The string tension was calculated and was found to have a jump at the
transition point. The value of \sigma is independent of L in the smooth phase,
while it increases with increasing L in the crumpled phase. This behavior of
\sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu,
where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled
phase. We should note that a possibility of a continuous transition is not
completely eliminated.Comment: 15 pages with 10 figure
Hamiltonian dynamics of the two-dimensional lattice phi^4 model
The Hamiltonian dynamics of the classical model on a two-dimensional
square lattice is investigated by means of numerical simulations. The
macroscopic observables are computed as time averages. The results clearly
reveal the presence of the continuous phase transition at a finite energy
density and are consistent both qualitatively and quantitatively with the
predictions of equilibrium statistical mechanics. The Hamiltonian microscopic
dynamics also exhibits critical slowing down close to the transition. Moreover,
the relationship between chaos and the phase transition is considered, and
interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure
Monte Carlo simulation of the Stillinger-Weber model for Si-Ge alloys
The bulk phase behavior of silicon-germanium alloys is investigated by means of constant pressure Monte Carlo simulation of the Stillinger-Weber potential in the semi-grand-conical ensemble. At low temperatures, Si and Ge phase separate into a Si-rich phase and a Ge-rich phase. The two-phase region is terminated by a critical point whose nature is investigated thoroughly by the multihistogram method combined with finite size scaling analysis. These results showed that the critical behavior of the alloy belongs to the mean field universality class, presumably due to the elastic degrees of freedom. We have also studied the structural properties of the mixture and found that the linear thermal expansions of both Si and Ge agree well with experiments. We also verified Vegard\u27s law above the critical point and calculated bond length distributions