3,526 research outputs found
Critical Exponents of the Four-State Potts Model
The critical exponents of the four-state Potts model are directly derived
from the exact expressions for the latent heat, the spontaneous magnetization,
and the correlation length at the transition temperature of the model.Comment: LaTex, 7 page
Mean Field Renormalization Group for the Boundary Magnetization of Strip Clusters
We analyze in some detail a recently proposed transfer matrix mean field
approximation which yields the exact critical point for several two dimensional
nearest neighbor Ising models. For the square lattice model we show explicitly
that this approximation yields not only the exact critical point, but also the
exact boundary magnetization of a semi--infinite Ising model, independent of
the size of the strips used. Then we develop a new mean field renormalization
group strategy based on this approximation and make connections with finite
size scaling. Applying our strategy to the quadratic Ising and three--state
Potts models we obtain results for the critical exponents which are in
excellent agreement with the exact ones. In this way we also clarify some
advantages and limitations of the mean field renormalization group approach.Comment: 16 pages (plain TeX) + 8 figures (PostScript, appended),
POLFIS-TH.XX/9
Potts-Percolation-Gauss Model of a Solid
We study a statistical mechanics model of a solid. Neighboring atoms are
connected by Hookian springs. If the energy is larger than a threshold the
"spring" is more likely to fail, while if the energy is lower than the
threshold the spring is more likely to be alive. The phase diagram and
thermodynamic quantities, such as free energy, numbers of bonds and clusters,
and their fluctuations, are determined using renormalization-group and
Monte-Carlo techniques.Comment: 10 pages, 12 figure
Application of exchange Monte Carlo method to ordering dynamics
We apply the exchange Monte Carlo method to the ordering dynamics of the
three-state Potts model with the conserved order parameter. Even for the deeply
quenched case to low temperatures, we have observed a rapid domain growth; we
have proved the efficiency of the exchange Monte Carlo method for the ordering
process. The late-stage growth law has been found to be for
the case of conserved order parameter of three-component system.Comment: 7 pages including 5 eps figures, to appear in New J. Phys.
http://www.njp.or
Integrability of the critical point of the Kagom\'e three-state Potts mode
The vicinity of the critical point of the three-state Potts model on a
Kagom\'e lattice is studied by mean of Random Matrix Theory. Strong evidence
that the critical point is integrable is given.Comment: 1 LaTex file + 3 eps files 7 page
The Cooperative Participatory Evaluation of Renewable Technologies on Ecosystem Services (CORPORATES)
Publisher PD
Internal Energy of the Potts model on the Triangular Lattice with Two- and Three-body Interactions
We calculate the internal energy of the Potts model on the triangular lattice
with two- and three-body interactions at the transition point satisfying
certain conditions for coupling constants. The method is a duality
transformation. Therefore we have to make assumptions on uniqueness of the
transition point and that the transition is of second order. These assumptions
have been verified to hold by numerical simulations for q=2, 3 and 4, and our
results for the internal energy are expected to be exact in these cases.Comment: 9 pages, 4 figure
Phase Structure of Z(3)-Polyakov-Loop Models
We study effective lattice actions describing the Polyakov loop dynamics
originating from finite-temperature Yang-Mills theory. Starting with a
strong-coupling expansion the effective action is obtained as a series of
Z(3)-invariant operators involving higher and higher powers of the Polyakov
loop, each with its own coupling. Truncating to a subclass with two couplings
we perform a detailed analysis of the statistical mechanics involved. To this
end we employ a modified mean field approximation and Monte Carlo simulations
based on a novel cluster algorithm. We find excellent agreement of both
approaches concerning the phase structure of the theories. The phase diagram
exhibits both first and second order transitions between symmetric,
ferromagnetic and anti-ferromagnetic phases with phase boundaries merging at
three tricritical points. The critical exponents nu and gamma at the continuous
transition between symmetric and anti-ferromagnetic phases are the same as for
the 3-state Potts model.Comment: 20 pages, 22 figure
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