scholarly journals The topological strong spatial mixing property and new conditions for pressure approximation

2017 ◽  
Vol 38 (5) ◽  
pp. 1658-1696 ◽  
Author(s):  
RAIMUNDO BRICEÑO
Keyword(s):  
Gibbs Measures ◽  
High Rate ◽  
Topological Pressure ◽  
Stat Phys ◽  
Cavity Method ◽  
Conditional Probabilities ◽  
Hard Constraints ◽  
Efficient Approximation Algorithm ◽  
Combinatorial Condition ◽  
Mixing Property

In the context of stationary $\mathbb{Z}^{d}$ nearest-neighbour Gibbs measures $\unicode[STIX]{x1D707}$ satisfying strong spatial mixing, we present a new combinatorial condition (the topological strong spatial mixing property) on the support of $\unicode[STIX]{x1D707}$ that is sufficient for having an efficient approximation algorithm for topological pressure. We establish many useful properties of topological strong spatial mixing for studying strong spatial mixing on systems with hard constraints. We also show that topological strong spatial mixing is, in fact, necessary for strong spatial mixing to hold at high rate. Part of this work is an extension of results obtained by Gamarnik and Katz [Sequential cavity method for computing free energy and surface pressure. J. Stat. Phys.137(2) (2009), 205–232], and Marcus and Pavlov [An integral representation for topological pressure in terms of conditional probabilities. Israel J. Math.207(1) (2015), 395–433], who gave a special representation of topological pressure in terms of conditional probabilities.

ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS

2010 ◽  
Vol 22 (10) ◽  
pp. 1147-1179 ◽  
Author(s):  
LUIS BARREIRA
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Present Stage ◽  
The Past ◽  
Recent Developments ◽  
General Sequences ◽  
Uniqueness Of Equilibrium

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

scholarly journals Про конструктивні описи мір Гіббса для моделі Поттса на дереві Келі

2021 ◽  
Vol 73 (7) ◽  
pp. 938-950
Author(s):  
M. Rahmatullaev ◽  
F. К. Rafikov ◽  
Sh. Kh. Azamov
Keyword(s):  
Ising Model ◽  
Cayley Tree ◽  
Gibbs Measures ◽  
Stat Phys

УДК 517.9 Розглядається модель Поттса на деревi Келi. Доведено iснування мiр Гiббса, побудованих аналогiчним методом iз [H. Akin, U. A. Rozikov, S. Temir, <em>A new set of limiting Gibbs measures for the Ising model on a Cayley tree</em>, J. Stat. Phys., <strong>142</strong>, № 2, 314 – 321 (2011)] i -трансляцiйно-iнварiантних мiр Гiббса для моделi Поттса на деревi Келi. Обчислено вiльнi енергiї цих мiр Гiббса.

Weak Gibbs measures: speed of convergence to entropy, topological and geometrical aspects

2016 ◽  
Vol 37 (7) ◽  
pp. 2313-2336 ◽  
Author(s):  
PAULO VARANDAS ◽  
YUN ZHAO
Keyword(s):  
Error Term ◽  
Large Deviation ◽  
Gibbs Measures ◽  
Topological Pressure ◽  
Local Entropy ◽  
Pointwise Dimension ◽  
Topological Characterization ◽  
Return Times ◽  
Subshifts Of Finite Type

In this paper we obtain exponential large-deviation bounds in the Shannon–McMillan–Breiman convergence formula for entropy in the case of weak Gibbs measures and topologically mixing subshifts of finite type. We also prove almost sure estimates for the error term in the convergence to entropy given by the Shannon–McMillan–Breiman formula for both uniformly and non-uniformly expanding shifts. Finally, we establish a topological characterization of large-deviation bounds for Gibbs measures and deduce some of their topological and geometrical aspects: the local entropy is zero and the topological pressure of positive measure sets is total. Some applications include large-deviation estimates for Lyapunov exponents, pointwise dimension and slow return times.

scholarly journals Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets

2015 ◽  
Vol 37 (1) ◽  
pp. 79-102 ◽  
Author(s):  
THIAGO BOMFIM ◽  
PAULO VARANDAS
Keyword(s):  
Large Deviations ◽  
Gibbs Measures ◽  
Rate Function ◽  
Topological Pressure ◽  
Hölder Continuous ◽  
Continuous Potential ◽  
Hyperbolic Flows ◽  
Time Averages ◽  
Set Of Points ◽  
Level 2

In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular, if$f$has an expanding repeller and$\unicode[STIX]{x1D719}$is a Hölder continuous potential, we prove that the topological pressure of the set of points whose accumulation values of Birkhoff averages belong to some interval$I\subset \mathbb{R}$can be expressed in terms of the topological pressure of the whole system and the large deviations rate function. As a byproduct we deduce that most irregular sets for maps with the specification property have topological pressure strictly smaller than the whole system. Some extensions to a non-uniformly hyperbolic setting, level-2 irregular sets and hyperbolic flows are also given.

scholarly journals Hidden Gibbs measures on shift spaces over countable alphabets

2019 ◽  
Vol 20 (04) ◽  
pp. 2050028
Author(s):  
Godofredo Iommi ◽  
Camilo Lacalle ◽  
Yuki Yayama
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Markov Shifts ◽  
Sofic Shifts ◽  
Uniqueness Of Equilibrium ◽  
Countable Markov Shifts ◽  
Generalized Gibbs Measures

We study the thermodynamic formalism for particular types of sub-additive sequences on a class of subshifts over countable alphabets. The subshifts we consider include factors of irreducible countable Markov shifts under certain conditions, which we call irreducible countable sofic shifts. We show the variational principle for topological pressure for some sub-additive sequences with tempered variation on irreducible countable sofic shifts. We also study conditions for the existence and uniqueness of invariant ergodic Gibbs measures and the uniqueness of equilibrium states. Applications are given to some dimension problems and study of factors of (generalized) Gibbs measures on certain subshifts over countable alphabets.

Structure of Palladium Single-Crystal Films Prepared by Flash Evaporation onto (001) NaCl Substrates

1970 ◽  
Vol 28 ◽  
pp. 456-457
Author(s):  
L. E. Murr ◽  
G. Wong
Keyword(s):  
Single Crystal ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
High Rate ◽  
Flash Evaporation ◽  
Optimum Load ◽  
Single Crystal Films ◽  
Crystal Films ◽  
A Current

Palladium single-crystal films have been prepared by Matthews in ultra-high vacuum by evaporation onto (001) NaCl substrates cleaved in-situ, and maintained at ∼ 350° C. Murr has also produced large-grained and single-crystal Pd films by high-rate evaporation onto (001) NaCl air-cleaved substrates at 350°C. In the present work, very large (∼ 3cm2), continuous single-crystal films of Pd have been prepared by flash evaporation onto air-cleaved (001) NaCl substrates at temperatures at or below 250°C. Evaporation rates estimated to be ≧ 2000 Å/sec, were obtained by effectively short-circuiting 1 mil tungsten evaporation boats in a self-regulating system which maintained an optimum load current of approximately 90 amperes; corresponding to a current density through the boat of ∼ 4 × 104 amperes/cm2.

Rapid Freezing of Freeze-Etch Specimens

1980 ◽  
Vol 38 ◽  
pp. 752-755
Author(s):  
A. Elgsaeter ◽  
T. Espevik ◽  
G. Kopstad
Keyword(s):  
Low Temperature ◽  
Metal Surface ◽  
Relative Velocity ◽  
Thermal Contact ◽  
High Rate ◽  
Rapid Freezing ◽  
Temperature Decrease ◽  
Freeze Etching

The importance of a high rate of temperature decrease (“rapid freezing”) when freezing specimens for freeze-etching has long been recognized1. The two basic methods for achieving rapid freezing are: 1) dropping the specimen onto a metal surface at low temperature, 2) bringing the specimen instantaneously into thermal contact with a liquid at low temperature and subsequently maintaining a high relative velocity between the liquid and the specimen. Over the last couple of years the first method has received strong renewed interest, particularily as the result of a series of important studies by Heuser and coworkers 2,3. In this paper we will compare these two freezing methods theoretically and experimentally.

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