48,495 research outputs found
Interface Tensions and Perfect Wetting in the Two-Dimensional Seven-State Potts Model
We present a numerical determination of the order-disorder interface tension,
\sod, for the two-dimensional seven-state Potts model. We find
\sod=0.0114\pm0.0012, in good agreement with expectations based on the
conjecture of perfect wetting. We take into account systematic effects on the
technique of our choice: the histogram method. Our measurements are performed
on rectangular lattices, so that the histograms contain identifiable plateaus.
The lattice sizes are chosen to be large compared to the physical correlation
length. Capillary wave corrections are applied to our measurements on finite
systems.Comment: 8 pages, LaTex file, 2 postscript figures appended, HLRZ 63/9
Hybrid Monte Carlo algorithm for the Double Exchange Model
The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of
classical degrees of freedom coupled to non self-interacting lattices fermions.
The diagonalization of the Hamiltonian matrix is avoided by introducing a
path-integral formulation of the problem, in Euclidean space-time. A
perfect action formulation allows to work on the continuum euclidean time,
without need for a Trotter-Suzuki extrapolation. To demonstrate the feasibility
of the method we study the Double Exchange Model in three dimensions. The
complexity of the algorithm grows only as the system volume, allowing to
simulate in lattices as large as on a personal computer. We conclude
that the second order paramagnetic-ferromagnetic phase transition of Double
Exchange Materials close to half-filling belongs to the Universality Class of
the three-dimensional classical Heisenberg model.Comment: 20 pages plus 4 postscript figure
Finite-size scaling and conformal anomaly of the Ising model in curved space
We study the finite-size scaling of the free energy of the Ising model on
lattices with the topology of the tetrahedron and the octahedron. Our
construction allows to perform changes in the length scale of the model without
altering the distribution of the curvature in the space. We show that the
subleading contribution to the free energy follows a logarithmic dependence, in
agreement with the conformal field theory prediction. The conformal anomaly is
given by the sum of the contributions computed at each of the conical
singularities of the space, except when perfect order of the spins is precluded
by frustration in the model.Comment: 4 pages, 4 Postscript figure
Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture
We present a functional renormalization group (fRG) formalism for interacting
fermions on lattices that captures the flow into states with commensurate
spin-density wave order. During the flow, the growth of the order parameter is
fed back into the flow of the interactions and all modes can be integrated out.
This extends previous fRG flows in the symmetric phase that run into a
divergence at a nonzero RG scale, i.e., that have to be stopped at the ordering
scale. We use the corresponding Ward identity to check the accuracy of the
results. We apply our new method to a model with two Fermi pockets that have
perfect particle-hole nesting. The results obtained from the fRG are compared
with those in random phase approximation.Comment: revised version; 24 pages, 12 figure
Disordered periodic systems at the upper critical dimension
The effects of weak point-like disorder on periodic systems at their upper
critical dimension D_c for disorder are studied. The systems studied range from
simple elastic systems with D_c=4 to systems with long range interactions with
D_c=2 and systems with D_c=3 such as the vortex lattice with dispersive elastic
constants. These problems are studied using the Gaussian Variational method and
the Functional Renormalisation Group. In all the cases studied we find a
typical ultra-slow loglog(x) growth of the asymptotic displacement correlation
function, resulting in nearly perfect translational order. Consequences for the
Bragg glass phase of vortex lattices are discussed.Comment: 12 RevTex pages, uses epsfig, 2 figure
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