104 research outputs found
Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models
As is known, at the Gibbs-Boltzmann equilibrium, the mean-field -state
Potts model with a ferromagnetic coupling has only a first order phase
transition when , while there is no phase transition for an
antiferromagnetic coupling. The same equilibrium is asymptotically reached when
one considers the continuous time evolution according to a Glauber dynamics. In
this paper we show that, when we consider instead the Potts model evolving
according to a discrete-time dynamics, the Gibbs-Boltzmann equilibrium is
reached only when the coupling is ferromagnetic while, when the coupling is
anti-ferromagnetic, a period-2 orbit equilibrium is reached and a stable
second-order phase transition in the Ising mean-field universality class sets
in for each component of the orbit. We discuss the implications of this
scenario in real-world problems.Comment: 6 pages, 6 figure
Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart
We consider an Ising competitive model defined over a triangular Husimi tree
where loops, responsible for an explicit frustration, are even allowed. After a
critical analysis of the phase diagram, in which a ``gas of non interacting
dimers (or spin liquid) - ferro or antiferromagnetic ordered state'' transition
is recognized in the frustrated regions, we introduce the disorder for studying
the spin glass version of the model: the triangular +/- J model. We find out
that, for any finite value of the averaged couplings, the model exhibits always
a phase transition, even in the frustrated regions, where the transition turns
out to be a glassy transition. The analysis of the random model is done by
applying a recently proposed method which allows to derive the upper phase
boundary of a random model through a mapping with a corresponding non random
one.Comment: 19 pages, 11 figures; content change
On Phase Transitions for -Adic Potts Model with Competing Interactions on a Cayley Tree
In the paper we considere three state -adic Potts model with competing
interactions on a Cayley tree of order two. We reduce a problem of describing
of the -adic Gibbs measures to the solution of certain recursive equation,
and using it we will prove that a phase transition occurs if and only if
for any value (non zero) of interactions. As well, we completely solve the
uniqueness problem for the considered model in a -adic context. Namely, if
then there is only a unique Gibbs measure the model.Comment: 12 pages, to appear in the Proceedings of the '2nd International
Conference on p-Adic Mathematical Physics' (Belgrade, 15-21 September 2005)
published by AIP Conference Proceeding
On dominant contractions and a generalization of the zero-two law
Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to
L^1(X,{\cf},\m) be two positive contractions such that . If
then for all n\in\bn. In the present paper we
generalize this result to multi-parameter contractions acting on . As an
application of that result we prove a generalization of the "zero-two" law.Comment: 10 page
Markov states and chains on the car algebra
We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes
Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
We propose the construction of a quantum Markov chain that corresponds to a “forward”
quantum Markov chain. In the given construction, the quantum Markov chain is defined as
the limit of finite-dimensional states depending on the boundary conditions. A similar construction
is widely used in the definition of Gibbs states in classical statistical mechanics. Using this
construction, we study the quantum Markov chain associated with an XY -model on a Cayley tree.
For this model, within the framework of the given construction, we prove the uniqueness of the
quantum Markov chain i.e., we show that the state is independent of the boundary conditions
On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three
In the present paper we study forward Quantum Markov Chains (QMC) defined on
a Cayley tree. Using the tree structure of graphs, we give a construction of
quantum Markov chains on a Cayley tree. By means of such constructions we prove
the existence of a phase transition for the XY-model on a Cayley tree of order
three in QMC scheme. By the phase transition we mean the existence of two now
quasi equivalent QMC for the given family of interaction operators
.Comment: 34 pages, 1 figur
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