160 research outputs found
Finite-Size Scaling for Quantum Criticality above the Upper Critical Dimension: Superfluid-Mott-Insulator Transition in Three Dimensions
Validity of modified finite-size scaling above the upper critical dimension
is demonstrated for the quantum phase transition whose dynamical critical
exponent is . We consider the -component Bose-Hubbard model, which is
exactly solvable and exhibits mean-field type critical phenomena in the
large- limit. The modified finite-size scaling holds exactly in that limit.
However, the usual procedure, taking the large system-size limit with fixed
temperature, does not lead to the expected (and correct) mean-field critical
behavior due to the limited range of applicability of the finite-size scaling
form. By quantum Monte Carlo simulation, it is shown that the same holds in the
case of N=1.Comment: 18 pages, 4 figure
Transfer matrix for spanning trees, webs and colored forests
We use the transfer matrix formalism for dimers proposed by Lieb, and
generalize it to address the corresponding problem for arrow configurations (or
trees) associated to dimer configurations through Temperley's correspondence.
On a cylinder, the arrow configurations can be partitioned into sectors
according to the number of non-contractible loops they contain. We show how
Lieb's transfer matrix can be adapted in order to disentangle the various
sectors and to compute the corresponding partition functions. In order to
address the issue of Jordan cells, we introduce a new, extended transfer
matrix, which not only keeps track of the positions of the dimers, but also
propagates colors along the branches of the associated trees. We argue that
this new matrix contains Jordan cells.Comment: 29 pages, 7 figure
Non-contractible loops in the dense O(n) loop model on the cylinder
A lattice model of critical dense polymers is considered for the
finite cylinder geometry. Due to the presence of non-contractible loops with a
fixed fugacity , the model is a generalization of the critical dense
polymers solved by Pearce, Rasmussen and Villani. We found the free energy for
any height and circumference of the cylinder. The density of
non-contractible loops is found for and large . The
results are compared with those obtained for the anisotropic quantum chain with
twisted boundary conditions. Using the latter method we obtained for any
model and an arbitrary fugacity.Comment: arXiv admin note: text overlap with arXiv:0810.223
First Order Phase Transition in the 3-dimensional Blume-Capel Model on a Cellular Automaton
The first order phase transition of the three-dimensional Blume Capel are
investigated using cooling algorithm which improved from Creutz Cellular
Automaton for the parameter value in the first order phase transition
region. The analysis of the data using the finite-size effect and the histogram
technique indicate that the magnetic susceptibility maxima and the specific
heat maxima increase with the system volume () at .Comment: 13 pages, 4 figure
Exactly solvable statistical model for two-way traffic
We generalize a recently introduced traffic model, where the statistical
weights are associated with whole trajectories, to the case of two-way flow. An
interaction between the two lanes is included which describes a slowing down
when two cars meet. This leads to two coupled five-vertex models. It is shown
that this problem can be solved by reducing it to two one-lane problems with
modified parameters. In contrast to stochastic models, jamming appears only for
very strong interaction between the lanes.Comment: 6 pages Latex, submitted to J Phys.
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