84,627 research outputs found
Mott transition in lattice boson models
We use mathematically rigorous perturbation theory to study the transition
between the Mott insulator and the conjectured Bose-Einstein condensate in a
hard-core Bose-Hubbard model. The critical line is established to lowest order
in the tunneling amplitude.Comment: 20 page
Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice
We use Monte Carlo techniques and analytical methods to study the phase
diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are
M species all with the same fugacity z and a nearest neighbor hard core
exclusion between unlike particles. Simulations show that for M greater or
equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M)
while for z > z_d(M) there are M demixed phases each consisting mostly of one
species. For M=2 there is a direct second order transition from the gas phase
to the demixed phase while for M greater or equal 3 the transition at z_d(M)
appears to be first order putting it in the Potts model universality class. For
M large, Pirogov-Sinai theory gives z_d(M) ~ M-2+2/(3M^2) + ... . In the
crystal phase the particles preferentially occupy one of the sublattices,
independent of species, i.e. spatial symmetry but not particle symmetry is
broken. For M to infinity this transition approaches that of the one component
hard cube gas with fugacity y = zM. We find by direct simulations of such a
system a transition at y_c ~ 0.71 which is consistent with the simulation
z_c(M) for large M. This transition appears to be always of the Ising type.Comment: 11 pages, 4 postscript figures (added in replacement), Physica A (in
press
Monte Carlo simulations of 2d hard core lattice gases
Monte Carlo simulations are used to study lattice gases of particles with
extended hard cores on a two dimensional square lattice. Exclusions of one and
up to five nearest neighbors (NN) are considered. These can be mapped onto hard
squares of varying side length, (in lattice units), tilted by some
angle with respect to the original lattice. In agreement with earlier studies,
the 1NN exclusion undergoes a continuous order-disorder transition in the Ising
universality class. Surprisingly, we find that the lattice gas with exclusions
of up to second nearest neighbors (2NN) also undergoes a continuous phase
transition in the Ising universality class, while the Landau-Lifshitz theory
predicts that this transition should be in the universality class of the XY
model with cubic anisotropy. The lattice gas of 3NN exclusions is found to
undergo a discontinuous order-disorder transition, in agreement with the
earlier transfer matrix calculations and the Landau-Lifshitz theory. On the
other hand, the gas of 4NN exclusions once again exhibits a continuous phase
transition in the Ising universality class -- contradicting the predictions of
the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found
to undergo a discontinuous phase transition.Comment: 13 pages, lots of figure
The random geometry of equilibrium phases
This is a (long) survey about applications of percolation theory in
equilibrium statistical mechanics. The chapters are as follows:
1. Introduction
2. Equilibrium phases
3. Some models
4. Coupling and stochastic domination
5. Percolation
6. Random-cluster representations
7. Uniqueness and exponential mixing from non-percolation
8. Phase transition and percolation
9. Random interactions
10. Continuum modelsComment: 118 pages. Addresses: [email protected]
http://www.mathematik.uni-muenchen.de/~georgii.html [email protected]
http://www.math.chalmers.se/~olleh [email protected]
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