LOW TEMPERATURE PROPERTIES OF THE BLUME–EMERY–GRIFFITHS (BEG) MODEL IN THE REGION WITH AN INFINITE NUMBER OF GROUND STATE CONFIGURATIONS

2000 ◽  
Vol 12 (06) ◽  
pp. 779-806 ◽  
Author(s):  
GASTÃO A. BRAGA ◽  
PAULO C. LIMA ◽  
MICHAEL L. O'CARROLL
Keyword(s):  
Low Temperature ◽  
Decay Rate ◽  
Infinite Number ◽  
Minimal Energy ◽  
Point Function ◽  
Parameter Region ◽  
Exponential Decay Rate ◽  
Polymer Expansion ◽  
Pure States ◽  
Beg Model

For the low temperature Blume–Emery–Griffiths Zd, d ≥2, lattice model taking site spin values 0, +1, -1 we construct, using a polymer expansion, two pure states in the parameter region [Formula: see text] where there are an infinite number of configurations with minimal energy. Each state is invariant under translation by two lattice spacings and the two states are related by a unit translation. Using analyticity techniques we show that the truncated n-point function decays exponentially with an n-independent lower bound on the decay rate. For the truncated two-point function, we find the exact exponential decay rate in the limit β→∞.

scholarly journals Decision Theory and large deviations for dynamical hypotheses tests: The Neyman-Pearson Lemma, Min-Max and Bayesian tests

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hermes H. Ferreira ◽  
Artur O. Lopes ◽  
Silvia R. C. Lopes
Keyword(s):  
Decision Theory ◽  
Large Deviations ◽  
Sample Size ◽  
Decay Rate ◽  
Thermodynamic Formalism ◽  
Exponential Decay Rate ◽  
Log Likelihood ◽  
Two Measures ◽  
Classical Hypothesis ◽  
The Ideal

<p style='text-indent:20px;'>We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different Hölder Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is that here the two measures are singular with respect to each other. Among other objectives, we are interested in the decay rate of the wrong decisions probability, when the sample size <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> goes to infinity. We show a dynamical version of the Neyman-Pearson Lemma displaying the ideal test within a certain class of similar tests. This test becomes exponentially better, compared to other alternative tests, when the sample size goes to infinity. We are able to present the explicit exponential decay rate. We also consider both, the Min-Max and a certain type of Bayesian hypotheses tests. We shall consider these tests in the log likelihood framework by using several tools of Thermodynamic Formalism. Versions of the Stein's Lemma and Chernoff's information are also presented.</p>

MAGNETIZATION OF THE PURE STATES IN THE p-SPIN INTERACTION MODEL

2004 ◽  
Vol 18 (04n05) ◽  
pp. 773-784
Author(s):  
M. TALAGRAND
Keyword(s):  
Low Temperature ◽  
Finite Number ◽  
Interaction Model ◽  
Spin Interaction ◽  
Rigorous Proof ◽  
Pure States ◽  
Number Of Cells

We study the magnetization of the pure states in (a suitable version of) the p-spin interaction model at low temperature. We give a rigorous proof of the phenomenon, discovered in 1 that (very roughly speaking), at a given level of accuracy, the set of sites decomposes in a finite number of cells on which the magnetization of any different pure states are uncorrelated.

scholarly journals Nonlinear Observer Design of the Generalized Rössler Hyperchaotic Systems via DIL Methodology

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yeong-Jeu Sun
Keyword(s):  
Exponential Stability ◽  
Decay Rate ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Observer Design ◽  
Nonlinear Observer ◽  
State Observation ◽  
Exponential Decay Rate ◽  
Error System ◽  
Hyperchaotic Systems

The generalized Rössler hyperchaotic systems are presented, and the state observation problem of such systems is investigated. Based on the differential inequality with Lyapunov methodology (DIL methodology), a nonlinear observer design for the generalized Rössler hyperchaotic systems is developed to guarantee the global exponential stability of the resulting error system. Meanwhile, the guaranteed exponential decay rate can be accurately estimated. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of proposed approach.

Characterization of Contact Damping and Frequency in Elastic-Plastic Contact

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Decay Rate ◽  
Closed Form ◽  
Natural Frequency ◽  
Compressive Load ◽  
Vibration Response ◽  
Elastic Plastic ◽  
Exponential Decay Rate ◽  
Damping Rate ◽  
Nonlinear Normal

Elastic-plastic interaction of a block of rough surface with a smooth plane is considered in this paper. The nonlinear normal vibration response of the block is examined when subject to an external compressive load. Free vibration response of the block is studied. The vibration response corresponds to the application of a constant compressive external load and the study yields closed-form equations for the contact damping rate and contact natural frequency. It is shown that vibration decay rate is constant as opposed to the exponential decay rate for the linear vibrating systems. Closed form equations relating contact damping rate and contact natural frequency to the surface parameters are given.

scholarly journals Assessment of Patellar Tendon Reflex Responses Using Second-Order System Characteristics

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Brett D. Steineman ◽  
Pavan Karra ◽  
Kiwon Park
Keyword(s):  
Decay Rate ◽  
Natural Frequency ◽  
Patellar Tendon ◽  
Exponential Decay ◽  
Second Order ◽  
Order System ◽  
Sample Population ◽  
Exponential Decay Rate ◽  
Tendon Reflex ◽  
Patellar Tendon Reflex

Deep tendon reflex tests, such as the patellar tendon reflex (PTR), are widely accepted as simple examinations for detecting neurological disorders. Despite common acceptance, the grading scales remain subjective, creating an opportunity for quantitative measures to improve the reliability and efficacy of these tests. Previous studies have demonstrated the usefulness of quantified measurement variables; however, little work has been done to correlate experimental data with theoretical models using entire PTR responses. In the present study, it is hypothesized that PTR responses may be described by the exponential decay rate and damped natural frequency of a theoretical second-order system. Kinematic data was recorded from both knees of 45 subjects using a motion capture system and correlation analysis found that the meanR2value was 0.99. Exponential decay rate and damped natural frequency ranges determined from the sample population were −5.61 to −1.42 and 11.73 rad/s to 14.96 rad/s, respectively. This study confirmed that PTR responses strongly correlate to a second-order system and that exponential decay rate and undamped natural frequency are novel measurement variables to accurately measure PTR responses. Therefore, further investigation of these measurement variables and their usefulness in grading PTR responses is warranted.

scholarly journals Interference stabilization of autoionizing states in molecular N2 studied by time- and angular-resolved photoelectron spectroscopy

2016 ◽  
Vol 194 ◽  
pp. 509-524 ◽  
Author(s):  
Martin Eckstein ◽  
Nicola Mayer ◽  
Chung-Hsin Yang ◽  
Giuseppe Sansone ◽  
Marc J. J. Vrakking ◽  
...  
Keyword(s):  
Decay Rate ◽  
Photoelectron Spectroscopy ◽  
Rydberg States ◽  
Electronic States ◽  
The Other ◽  
Photoelectron Spectra ◽  
Angular Distributions ◽  
Velocity Map Imaging ◽  
Imaging Spectrometer ◽  
Exponential Decay Rate

An autoionizing resonance in molecular N2 is excited by an ultrashort XUV pulse and probed by a subsequent weak IR pulse, which ionizes the contributing Rydberg states. Time- and angular-resolved photoelectron spectra recorded with a velocity map imaging spectrometer reveal two electronic contributions with different angular distributions. One of them has an exponential decay rate of 20 ± 5 fs, while the other one is shorter than 10 fs. This observation is interpreted as a manifestation of interference stabilization involving the two overlapping discrete Rydberg states. A formalism of interference stabilization for molecular ionization is developed and applied to describe the autoionizing resonance. The results of calculations suggest, that the effect of the interference stabilization is facilitated by rotationally-induced couplings of electronic states with different symmetry.

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