Critical Behavior Of Phase Transition Research Articles

The mixed-state entanglement in holographic p-wave superconductor model

In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Furthermore, we explore the behavior of thermodynamics and holographic quantum information at the zeroth-order phase transition point and find that it is opposite to that observed in the first-order phase transition. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Our findings also suggest that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Lastly, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.

Magnetism in quasi-two-dimensional tri-layer La2.1Sr1.9Mn3O10 manganite

The tri-layer La_{3-3x}Sr_{1+3x}Mn_{3}O_{10} manganites of Ruddlesden–Popper (RP) series are naturally arranged layered structure with alternate stacking of ω-MnO_2 (ω = 3) planes and rock-salt type block layers (La, Sr)_2O_2 along c-axis. The dimensionality of the RP series manganites depends on the number of perovskite layers and significantly affects the magnetic and transport properties of the system. Generally, when a ferromagnetic material undergoes a magnetic phase transition from ferromagnetic to paramagnetic state, the magnetic moment of the system becomes zero above the transition temperature (T _{C} ). However, the tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10} shows non-zero magnetic moment above T _{C} and also another transition at higher temperature T ^{*} approx 263 K. The non-zero magnetization above T _{C} emphasizes that the phase transition in tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10} not a ferromagnetic to paramagnetic state. We show here the non-zero magnetic moment above T _{C} is due to the quasi-two-dimensional nature of the tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10} manganite. The scaling of the magnetic entropy change confirms the second-order phase transition and the critical behavior of phase transition has been studied around T_C to understand the low dimensional magnetism in tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10}. We have obtained the critical exponents for tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10}, which belong to the short-range two-dimensional (2D)-Ising universality class. The low dimensional magnetism in tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10} manganite is also explained with the help of renormalization group theoretical approach for short-range 2D-Ising systems. It has been shown that the layered structure of tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10} results in three different types of interactions intra-planer ( J_{ab} ), intra-tri-layer ( J_{c} ) and inter-tri-layer ( J' ) such that J_{ab}> J_{c}>> J' and competition among these give rise to the canted antiferromagnetic spin structure above T _{C} . Based on the similar magnetic interaction in bi-layer manganite, we propose that the tri-layer La_{2.1}Sr_{1.9}Mn_{3}O_{10} should be able to host the skyrmion below T _{C} due to its strong anisotropy and layered structure.

Analysis of thermodynamic problems with the Lambert W function

We present an analysis of two problems in thermodynamics in terms of the Lambert W function, including the mean-field approximation of the Ising model, and Bose–Einstein condensation. Both problems are well known to exhibit the critical behavior of phase transition. Standard treatment of the problems involves numerical or graphical solutions. Utilizing justified simplifying approximations, we find a closed-form mean-field solution for the Ising model in terms of the special W function. With the same special function, we present an analysis of Bose–Einstein condensation, allowing approximate quantitative determination of the dependence of the chemical potential on temperature without full numerical computation. The analysis helps to facilitate understanding and to gain insight on these processes involving phase transitions in a straightforward manner.

Matter wave interference of dilute Bose gases in the critical regime**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504328, 11274024, and 11334001) and the National Basic Research Program of China (Grants Nos. 2013CB921903 and 2012CB921300).

Ultra-cold atomic gases provide a new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science 315 1556 (2007)]. Our theory paves the way to experimentally study various types of ultra-cold atomic gases with the means of matter wave interference.

Phase transitions for rock-scissors-paper game on different networks

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in the rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and annealed randomness simultaneously. In the resulting phase diagrams three different stationary states are identified for all structures. The comparison of results on different networks suggests that the value of the clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase. The critical behavior of phase transitions seems to be universal and can be described by the same exponents.

Studies on the critical phase-transition behavior of cholestericN-phthaloyl chitosan/dimethyl sulfoxide solutions by five techniques

A selectively side-modified chitosan derivative, N-phthaloyl chitosan (PhthCs), was prepared. Five techniques, including circular dichroism (CD) spectropolarimetry, ultraviolet–visible (UV–vis) spectroscopy, small-angle light scattering (SALS), polarized optical microscopy (POM), and differential scanning calorimetry (DSC), were simultaneously applied to investigate the order–disorder phase transition for the lyotropic PhthCs/dimethyl sulfoxide system. POM observations suggested that the critical concentration was 48 wt %, which agreed well with the DSC measurements. A four-leaf SALS picture was recorded in biphasic solutions. The four-leaf type became a circular symmetric scattering picture with a further increase in the concentration. A sharp peak at 330 nm was recorded in dilute isotropic solutions with CD measurements. The sharp peak turned into a broad tailed peak from 330 to 800 nm after the phase transition occurred. The sharp peak was induced by a chromophore (phthoyl group). The broad peak was attributed to the formation of short-range-ordered organization in the concentrated solutions. In UV–vis studies, when the system varied from isotropic to anisotropic, the absorption band turned into platform. These five techniques were proven to be feasible methods for measuring the phase transition of cholesteric liquid crystals. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 583–586, 2003

Scaling and Critical Behavior of Phase Transitions in Ising Strips and Nanotubes

Phase transitions in strips of dimensions (D,L), with L»D, have been investigated by means of Monte Carlo numerical simulations. Strips have been studied under free boundary conditions and folded in a nanotube shape using periodic boundary conditions. Numerical simulations for different (D,L) values have been performed to study the width (D) dependence of the critical temperature. The general features of the phase transitions in Ising strips and nanotubes are discussed.

Scaling and Critical Behavior of Phase Transitions in Ising Strips and Nanotubes

Phase transitions in strips of dimensions (D,L), with L>>D, have been investigated by means of Monte Carlo numerical simulations. Strips have been studied under free boundary conditions and folded in a nanotube shape using periodic boundary conditions. Numerical simulations for different (D,L) values have been performed to study the width (D) dependence of the critical temperature. The general features of the phase transitions in Ising strips and nanotubes are discussed.

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Within the four-loop $\ve$ expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality $N_c^C=1.445(20)$ obtained from six loops via the exact relation $N_c^C={1/2} N_c^R$ established for the real and complex hypercubic models.

Phase transition related stress in ferroelectric thin films

An uneven distribution of stress in the thickness direction was introduced into Landau theory to investigate the critical behavior of phase transition of ferroelectric thin films. The Curie temperature T C was calculated to increase and decrease for compressive and tensile stress cases, respectively. The dispersion of phase transition was predicted. The diffusivity increased with stress, but showed a non-monotonic relation to film thickness. The results of the calculations were compared with some experimental results.

Critical behavior of phase transitions in potassium-dihydrogen-phosphate-type ferroelectrics.

Critical behavior of phase transitions in potassium-dihydrogen-phosphate-type ferroelectrics.

Report: Nonequilibrium Phase Transitions of Impact Ionization Breakdown in Extrinsic Semiconductors

Abstract In the study of semiconductor electronic breakdown we observe the self-generated formation of spatio-temporal dissipative structures, when a bias voltage is applied at liquid-helium temperature. The underlying nonlinear physics of impurity impact ionization reveals critical phase transition behavior by varying the temperature at constant voltage