37 research outputs found
Effective interactions due to quantum fluctuations
Quantum lattice systems are rigorously studied at low temperatures. When the
Hamiltonian of the system consists of a potential (diagonal) term and a - small
- off-diagonal matrix containing typically quantum effects, such as a hopping
matrix, we show that the latter creates an effective interaction between the
particles.
In the case that the potential matrix has infinitely many degenerate ground
states, some of them may be stabilized by the effective potential. The low
temperature phase diagram is thus a small deformation of the zero temperature
phase diagram of the diagonal potential and the effective potential. As
illustrations we discuss the asymmetric Hubbard model and the hard-core
Bose-Hubbard model.Comment: 35 pages, AMSLate
Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models
We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices
Metastability and Nucleation for the Blume-Capel Model. Different mechanisms of transition
We study metastability and nucleation for the Blume-Capel model: a
ferromagnetic nearest neighbour two-dimensional lattice system with spin
variables taking values in -1,0,+1. We consider large but finite volume, small
fixed magnetic field h and chemical potential "lambda" in the limit of zero
temperature; we analyze the first excursion from the metastable -1
configuration to the stable +1 configuration. We compute the asymptotic
behaviour of the transition time and describe the typical tube of trajectories
during the transition. We show that, unexpectedly, the mechanism of transition
changes abruptly when the line h=2*lambda is crossed.Comment: 96 pages, 44 tex-figures, 7 postscript figure
Critical droplets in Metastable States of Probabilistic Cellular Automata
We consider the problem of metastability in a probabilistic cellular
automaton (PCA) with a parallel updating rule which is reversible with respect
to a Gibbs measure. The dynamical rules contain two parameters and
which resemble, but are not identical to, the inverse temperature and external
magnetic field in a ferromagnetic Ising model; in particular, the phase diagram
of the system has two stable phases when is large enough and is
zero, and a unique phase when is nonzero. When the system evolves, at small
positive values of , from an initial state with all spins down, the PCA
dynamics give rise to a transition from a metastable to a stable phase when a
droplet of the favored phase inside the metastable phase reaches a
critical size. We give heuristic arguments to estimate the critical size in the
limit of zero ``temperature'' (), as well as estimates of the
time required for the formation of such a droplet in a finite system. Monte
Carlo simulations give results in good agreement with the theoretical
predictions.Comment: 5 LaTeX picture
Short-time Gibbsianness for Infinite-dimensional Diffusions with Space-Time Interaction
We consider a class of infinite-dimensional diffusions where the interaction
between the components is both spatial and temporal. We start the system from a
Gibbs measure with finite-range uniformly bounded interaction. Under suitable
conditions on the drift, we prove that there exists such that the
distribution at time is a Gibbs measure with absolutely summable
interaction. The main tool is a cluster expansion of both the initial
interaction and certain time-reversed Girsanov factors coming from the
dynamics
Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree
We consider models with nearest-neighbor interactions and with the set
of spin values, on a Cayley tree of order .
It is known that the "splitting Gibbs measures" of the model can be described
by solutions of a nonlinear integral equation. For arbitrary we find
a sufficient condition under which the integral equation has unique solution,
hence under the condition the corresponding model has unique splitting Gibbs
measure.Comment: 13 page
A model with simultaneous first and second order phase transitions
We introduce a two dimensional nonlinear XY model with a second order phase
transition driven by spin waves, together with a first order phase transition
in the bond variables between two bond ordered phases, one with local
ferromagnetic order and another with local antiferromagnetic order. We also
prove that at the transition temperature the bond-ordered phases coexist with a
disordered phase as predicted by Domany, Schick and Swendsen. This last result
generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue
that these phenomena are quite general and should occur for a large class of
potentials.Comment: 7 pages, 7 figures using pstricks and pst-coi
Monte Carlo with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics
A class of Monte Carlo algorithms which incorporate absorbing Markov chains
is presented. In a particular limit, the lowest-order of these algorithms
reduces to the -fold way algorithm. These algorithms are applied to study
the escape from the metastable state in the two-dimensional square-lattice
nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the
agreement with theoretical predictions is very good. It is demonstrated that
the higher-order algorithms can be many orders of magnitude faster than either
the traditional Monte Carlo or -fold way algorithms.Comment: ReVTeX, Request 3 figures from [email protected]