The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

Formation of Periodic Ripples in a Surface Skin

1977 ◽  
Vol 32 (1) ◽  
pp. 33-39
Author(s):  
Fred Fischer
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Liquid Surface ◽  
Compressive Strain ◽  
Critical Value ◽  
Skin Thickness ◽  
Skin Area ◽  
Ripple Formation ◽  
Elastic Skin ◽  
Second Order Phase Transition

Abstract A solid elastic skin on a liquid surface aquires a periodic ripple formation when a compressive strain surpasses a critical value. From a calculation the ripple wavelength is found to be proportional to the 3/4th power of the skin thickness. This instability can be described as a kind of second order phase transition, where a relative amplitude of the ripple wave is the order parameter. In addition, when the skin area is abruptly compressed the ripple wavelength depends on the magnitude of the compressive strain. Examples for skin rippling with wavelengths between 10 μm and 100 m are discussed.

CRITICAL BEHAVIOR OF THE SPECIFIC HEAT IN THE VICINITY OF THE TRANSITION TEMPERATURE FOR S-TRIAZINE

2009 ◽  
Vol 23 (09) ◽  
pp. 2253-2259 ◽  
Author(s):  
M. KURT ◽  
H. YURTSEVEN
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Transition Temperature ◽  
Critical Exponent ◽  
Specific Heat ◽  
Power Law ◽  
Order Phase Transition ◽  
Critical Behavior ◽  
First Order ◽  
Second Order Phase Transition

The critical behavior of the specific heat is studied in s-triazine ( C 3 N 3 H 3). Using the experimental data for the CP, the temperature dependence of the specific heat is analyzed according to a power-law formula and the values of the critical exponent for CP are extracted in the vicinity of the transition temperature (TC=198.07 K ). It is indicated that s-triazine undergoes a weakly first order (quasi-continuous) or second order phase transition.

Target excitation dependence of degree of multifractality and critical exponent in ultrarelativistic nuclear collision

2010 ◽  
Vol 88 (9) ◽  
pp. 651-656 ◽  
Author(s):  
Dipak Ghosh ◽  
Argha Deb ◽  
Ruma Saha ◽  
Rupa Das
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Phase Transition ◽  
Particle Density ◽  
Nuclear Collision ◽  
Particle Density Distribution ◽  
Thermal Phase Transition ◽  
Thermal Phase ◽  
Show Evidence ◽  
Second Order Phase Transition

The target excitation dependence of the degree of multifractality and critical exponent of pions produced for the 16O-AgBr interaction at 60 AGeV has been investigated. To study target excitation dependence, the data for the produced pions were distributed into three sets, depending on the number of grey tracks (ng). The different sets correspond to the different degrees of target excitation. The probability G-moments were used for the analysis in pseudorapidity space. The analysis reveals that the produced particle density distribution possesses multifractal structure for all degrees of target excitation (0 ≤ ng ≤ 3, 4 ≤ ng ≤ 7, and ng ≥ 8). The distribution Levy index and the phase transition critical exponent are calculated. The study indicates the non-thermal phase transition, but it does not show evidence for the second-order phase transition.

Behavioral transitions induced by speed and noise in animal aggregates

2017 ◽  
Vol 31 (11) ◽  
pp. 1750073 ◽  
Author(s):  
Dorílson S. Cambui ◽  
Tarras Iliass
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Collective Behavior ◽  
Order Parameter ◽  
Finite Size ◽  
Particle Model ◽  
Collective State ◽  
Finite Size Scaling ◽  
Behavioral Transitions ◽  
Binder Cumulant

In this paper, we used a self-propelled particle model to study the transition between phases of collective behavior observed in animal aggregates. In these systems, transitions occur when individuals shift from one collective state to another. We investigated transitions induced by both the speed and the noise. Statistical quantities that characterize the phase transition driven by noise, such as order parameter, the Binder cumulant and the susceptibility were analyzed, and we used the finite-size scaling theory to estimate the critical exponent ratios [Formula: see text] and [Formula: see text].

scholarly journals ON THE THERMAL PHASE STRUCTURE OF QCD AT VANISHING CHEMICAL POTENTIALS

2011 ◽  
Vol 26 (18) ◽  
pp. 3035-3050 ◽  
Author(s):  
SONIA KABANA ◽  
PETER MINKOWSKI
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Energy Density ◽  
Order Parameter ◽  
Thermal Structure ◽  
Boson Pair ◽  
Chemical Potentials ◽  
Consistent Model ◽  
Thermal Phase ◽  
Second Order Phase Transition

The hypothesis is investigated, that the thermal structure of QCD phases at and near zero chemical potentials is determined by long range coherence, inducing the gauge boson pair condensate, and its thermal extension, representing a fundamental order parameter. A consistent model for thermal behavior including interactions is derived in which the condensate does not produce any latent heat as it vanishes at the critical temperature inducing a second-order phase transition with respect to energy density neglecting eventual numerically small critical exponents. Localization and delocalization of color fields are thus separated by a unique critical temperature.

scholarly journals TIME REVERSAL BREAKING SUPERCONDUCTING STATE IN THE PHASE DIAGRAM OF THE CUPRATES

2003 ◽  
Vol 17 (04n06) ◽  
pp. 614-620 ◽  
Author(s):  
G. SANGIOVANNI ◽  
M. CAPONE ◽  
S. CAPRARA
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Order Phase Transition ◽  
Superconducting State ◽  
Time Reversal ◽  
Low Temperatures ◽  
Order Parameter ◽  
Andreev Reflection ◽  
Previous Analysis ◽  
Second Order Phase Transition

We review and extend a previous study1 on the symmetry of the superconducting state, stimulated by recent tunneling and Andreev reflection measurements giving robust evidences for the existence of a dx2-y2 + idxy order parameter in the overdoped regime of two different cuprates. Looking for a possible second-order phase transition from a standard dx2-y2 to a mixed and time reversal breaking state, we confirm the results of our previous analysis on La 2-x Sr x CuO 4. In the case of Y 1-y Ca y Ba 2 Cu 3 O 7-x as well, among all the allowed symmetries, the dx2 - y2 + idxy is the most favored one and the unconventional state is likely to occur in a small dome of the phase diagram located in the optimal-overdoped region and at very low temperatures.

The order parameter critical exponent of the chiral phase transition in

2007 ◽  
Vol 310 (2) ◽  
pp. 1410-1412
Author(s):  
F. Ye ◽  
Y.W. Rodriguez ◽  
D.P. Belanger ◽  
J.A. Fernandez-Baca
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Chiral Phase ◽  
Chiral Phase Transition
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