Theory Of Phase Transitions Research Articles

Theory of nematic-isotropic phase transitions in solutions of rodlike aggregates

ABSTRACT A mean-field theory is introduced to describe phase behaviours for solutions of rodlike aggregates. By combining the Onsager model for rodlike aggregates and the Flory-Huggins model for polydisperse polymer solutions, we derive the free energy for the solutions of the rodlike aggregates. We calculate the mean aggregation number and orientational order parameter of rodlike aggregates. The mean aggregation number jumps at the first-order nematic–isotropic transition (NIT). We also derive the Landau-de Gennes expansion of the free energy and calculate the isotropic-nematic coexistence curves on the temperature-concentration plane. The NIT curves are qualitatively consistent with the experimental results of rodlike aggregates.

Strange Metal and Superconductor in the Two-Dimensional Yukawa-Sachdev-Ye-Kitaev Model.

The two-dimensional Yukawa-Sachdev-Ye-Kitaev (2D-YSYK) model provides a universal theory of quantum phase transitions in metals in the presence of quenched random spatial fluctuations in the local position of the quantum critical point. It has a Fermi surface coupled to a scalar field by spatially random Yukawa interactions. We present full numerical solutions of a self-consistent disorder averaged analysis of the 2D-YSYK model in both the normal and superconducting states, obtaining electronic spectral functions, frequency-dependent conductivity, and superfluid stiffness. Our results reproduce key aspects of observations in the cuprates as analyzed by Michon etal. [Nat. Commun. 14, 3033 (2023)NCAOBW2041-172310.1038/s41467-023-38762-5]. We also find a regime of increasing zero temperature superfluid stiffness with decreasing superconducting critical temperature, as is observed in bulk cuprates.

Controlling Matter Phases beyond Markov.

Controlling phase transitions in quantum systems via coupling to reservoirs has been mostly studied for idealized memory-less environments under the so-called Markov approximation. Yet, most quantum materials and experiments in the solid state, atomic, molecular and optical physics are coupled to reservoirs with finite memory times. Here, using the spectral theory of non-Markovian dissipative phase transitions developed in the companion paper [Debecker, Martin, and Damanet (to be published)], we show that memory effects can be leveraged to reshape matter phase boundaries, but also reveal the existence of dissipative phase transitions genuinely triggered by non-Markovian effects.

Spectral theory of non-Markovian dissipative phase transitions

Spectral theory of non-Markovian dissipative phase transitions

Nonlinear soliton spiral induces coupled multimode dynamics in multi-stable dissipative metamaterials

With the robust and self-trapped properties, recent advances about soliton dynamics in multi-stable mechanical metamaterials have led to many innovative techniques from signal processing to robotics. This work proposes a multi-stable mechanical metamaterial driven by nonlinear dissipative solitons, in which the coupling and decoupling of multiple locomotion modes can be achieved. Based on a cylinder network with asymmetric energy landscape, the uniform field model of Landau theory is developed. During the theoretical calculation, the analytical solutions of several dissipative solitons are derived, which allow multiple special behaviors of solitary waves, such as wave velocity gaps, directional propagation and spiral phase transition. By incorporating such effects into robotic designs, a variety of complex movements can be achieved by a single structure, including hopping, rolling, rotating, swinging, bending and translational components. In particular, as excitation positions change, the mechanical metamaterial can flexibly switch multiple locomotion modes without changing configurations, e.g., spinning and spin-less, straight and oblique as well as coupled multimode movements. This work wishes to provide some new inspirations for the applications of nonlinear elastic wave metamaterials and phase transition theory in robotics.

A 3D finite deformation constitutive model for anisotropic shape memory polymer composites integrating viscoelasticity and phase transition concept

The phase transition theory of shape memory polymers (SMPs) often involves a phenomenological assumption that the reference configuration of the newly transformed phase deviates from that of the initial phase. This distinction serves as a crucial mechanism in the manifestation of the shape memory effect. However, elucidating the precise definition of the reference configuration of the transformed phase poses a significant challenge in the formulation of the constitutive model. To tackle this challenge, a three-dimensional (3D) finite deformation constitutive model incorporating effective phase evolution for SMPs has been developed. This model merges insights from the classical viscoelastic framework with the phase transition theory. The anisotropic thermo-viscoelastic constitutive model is further developed by introducing hyperelastic fibers, which integrate the anisotropy of the fibers into a continuous thermodynamic framework through structure tensors. Implemented within the ABAQUS software via a user material (UMAT) subroutine, the proposed model has been meticulously validated against experimental data, showcasing its prowess in simulating stress-strain responses and shape memory characteristics of SMPs and their composites (SMPCs). This innovative model stands as an invaluable instrument for the design and of sophisticated SMP and SMPC structures.

First-principles study of Ti adsorption on Al4C3 (0001) surface

Al4C3 phase is hypothesized to undergo a solid–solid phase transition into TiC, thereby facilitating the heterogeneous nucleation of α-Al. However, capturing this transition process experimentally is challenging, which undermines the credibility of this transition theory. In this study, first-principles calculations are employed to investigate the feasibility of Ti atom adsorption on the exposed (0001) surface of the Al4C3 crystal, providing theoretical support for the phase transition hypothesis. The findings indicate that Ti adatoms can effectively adsorb on the C-terminated (0001) surface, whereas adsorption on the Al-terminated surface is thermodynamically unfavorable. Upon structural optimization, Ti adatoms at bridge site B, top site T, and hollow site H1, irrespective of coverage, migrate towards the most stable hollow H2 site. Electronic structure analysis reveals that the bonding between the Ti adatom at the H2 site and the surface layer C atoms is primarily covalent, while the bonding with subsurface layer Al atoms is metallic. Additionally, Ti atom adsorption induces polarization of the bonding electron cloud between Al and C atoms. This study provides theoretical support for the Ti-induced transformation of the Al4C3 to TiC phase via surface adsorption, paving the way for the development of high-performance master alloys based on phase transition theory.

Effect of arm-length polydispersity on the phase behaviour of V-shaped molecules

Phase behaviour of a melt of polydisperse V-shaped particles is considered within the Landau theory of phase transitions. It is assumed that particles are composed of two semi-flexible segments, one of which has a constant length, while the other has an arbitrary length distribution; the segments are joined at an external angle. The contributions up to the sixth order into the Landau–de Gennes free energy expansion in terms of the alignment tensor are presented in a diagrammatic form. The phase diagrams have been obtained for a special case characterised by rigid segments and Schulz–Zimm distribution for the length of the segment. It is shown that an increase in the polydispersity index of the segment leads to an increase of the isotropic–nematic transition temperature, substantial increase of the stability region of a uniform biaxial nematic ( N B ) phase, and a decrease in the area occupied by a uniform oblate nematic phase.

Why and how did the COVID pandemic end abruptly?

Phase transition theory, implemented quantitatively by thermodynamic scaling, has explained the evolution of Coronavirus’ extremely high contagiousness caused by a few key mutations from CoV2003 to CoV2019 identified among hundreds, as well as the later 2021 evolution to Omicron caused by 30 mutations. It also showed that the 2022 strain BA.5 with five mutations began a new path. Here we show that the early 2023 strains BKK with one stiffening mutation confirm that path, and the single flexing mutation of a later 2023 variant EG.5 strengthens it further. The few mutations of the new path have greatly reduced pandemic deaths, for mechanical reasons proposed here.Graphical abstractSurprisingly abrupt drop in COVID death rate

A simplex path integral and a simplex renormalization group for high-order interactions *

Modern theories of phase transitions and scale invariance are rooted in path integral formulation and renormalization groups (RGs). Despite the applicability of these approaches in simple systems with only pairwise interactions, they are less effective in complex systems with undecomposable high-order interactions (i.e. interactions among arbitrary sets of units). To precisely characterize the universality of high-order interacting systems, we propose a simplex path integral and a simplex RG (SRG) as the generalizations of classic approaches to arbitrary high-order and heterogeneous interactions. We first formalize the trajectories of units governed by high-order interactions to define path integrals on corresponding simplices based on a high-order propagator. Then, we develop a method to integrate out short-range high-order interactions in the momentum space, accompanied by a coarse graining procedure functioning on the simplex structure generated by high-order interactions. The proposed SRG, equipped with a divide-and-conquer framework, can deal with the absence of ergodicity arising from the sparse distribution of high-order interactions and can renormalize a system with intertwined high-order interactions at the p-order according to its properties at the q-order ( p⩽q ). The associated scaling relation and its corollaries provide support to differentiate among scale-invariant, weakly scale-invariant, and scale-dependent systems across different orders. We validate our theory in multi-order scale-invariance verification, topological invariance discovery, organizational structure identification, and information bottleneck analysis. These experiments demonstrate the capability of our theory to identify intrinsic statistical and topological properties of high-order interacting systems during system reduction.

Applying network-free renormalization and clustering algorithms to reveal the crack evolution laws of laterally loaded composite T-joints

Delamination or crack are standard failure patterns of composite T-joints. Most existing studies focus on pull-off loaded composite T-joint cracking but little focus on adverse conditions such as lateral loading. The mainstream composite T-joint research predicts the macroscale failure based on the composite’s microscale/mesoscale crack starting and evolution. However, the cracking process is within the microscale, mesoscale, and macroscale, making detecting its starting based on phenomena complicated. This work attempts to directly model the macroscale deformation distribution from a thermodynamic perspective to reveal the cracking/failure evolution of a laterally loaded composite T-joint. Firstly, we conducted eight laterally loaded composite T-joint tests with different molding processes. Then, network-free renormalization was applied to construct Matrices (Modes) and Hamiltonians (Characteristic parameters) that can characterize their cracking evolution process. Further, a clustering algorithm was applied to reveal the cracking starting points (phase transition loads) embedded in the macroscale deformation distribution. We can verify its rationality by comparing the composite T-joints localized and systematic phase transition loads based on Wilson’s phase transition theory. In summary, this work applies network-free renormalization and clustering algorithms from a thermodynamic perspective to reveal the cracking starting point embedded in the macroscale deformation distribution of the laterally loaded composite T-joints.

Investigation into the DNA's conformations and their conversions from the phase transition theory

The functions and transformation mechanisms of nucleic acids in their various states are of great importance in physiology and pathology. Based on the Landau model, this study reveals the mechanism of the existence of chirality and the transformation rules between different chiral conformations by studying the Duffing oscillation response of the local gauge potential on the DNA chain. The research results show that normal chiral DNA and DNA configuration transition behaviors exhibit regular nonlinear periodic oscillations. Moreover, the gauge potential value approaches zero at the B-Z junction site, which may add a criterion for detecting Z-forming sites. In addition, external force and damping play a key role in the chiral gauge potential of nucleic acids, and they can influence, regulate and even control the configuration transition of nucleic acids. Finally, we verified the rationality of our theory by combining x-ray crystal diffraction data of multiple configurations of DNA. This study provides new insights into the behavior and function of chiral DNA in organisms, and provides new possibilities for regulating DNA conformational transition in the future.

Optical pulse-induced ultrafast antiferrodistortive transition in SrTiO3

The ultrafast dynamics of the antiferrodistortive phase transition in perovskite SrTiO3 is monitored via time-domain Brillouin scattering. Using femtosecond optical pulses, we initiate a thermally driven tetragonal-to-cubic structural transformation and detect the crystal phase through changes in the frequency of Brillouin oscillations (BO) induced by propagating acoustic phonons. Coupling the measured BO frequency with a spatiotemporal heat diffusion model, we demonstrate that, for a sample kept in the tetragonal phase, deposition of sufficient thermal energy induces a rapid transformation of the heat-affected region to the cubic phase. The initial phase change is followed by a slower reverse cubic-to-tetragonal phase transformation occurring on a timescale of hundreds of picoseconds. We attribute this ultrafast phase transformation in the perovskite to a structural resemblance between atomic displacements of the R-point soft optic mode of the cubic phase and the tetragonal phase, both characterized by anti-phase rotation of oxygen octahedra. The structural relaxation time exhibits a strong temperature dependence consistent with the prediction of the equation of motion describing collective oxygen octahedra rotation based on the energy landscape of the phenomenological Landau theory of phase transitions. Evidence of such a fast structural transition in perovskites can open up new avenues in information processing and energy storage sectors.

Antiferroelectric Ceramics for Energy-Efficient Capacitors by Theory-Guided Discovery.

Antiferroelectric ceramics, via the electric-field-induced antiferroelectric (AFE)-ferroelectric (FE) phase transitions, show great promise for high-energy-density capacitors. Yet, currently, only 70-80% energy release is found during a charge-discharge cycle. Here, for PbZrO3-based oxides, geometric nonlinear theory of martensitic phase transitions is applied (first used to guide supercompatible shape-memory alloys) to predict the reversibility of the AFE-FE transition by using density-functional theory to assess AFE/FE interfacial lattice-mismatch strain that assures ultralow electric hysteresis and extended fatigue lifetime. A good correlation of mismatch strain with electric hysteresis, hence, with energy efficiency of AFE capacitors is observed. Guided by theory, high-throughput material search is conducted and AFE compositions with a near-perfect charge-discharge energy efficiency (98.2%), i.e., near-zero hysteresis are discovered. And the fatigue life of the capacitor reaches 79.5 million charge-discharge cycles, a factor of 80 enhancement over AFE ceramics with large electric hysteresis.

Quantum scaling for the metal–insulator transition in a two-dimensional electron system

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase’s resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.

To the theory of phase transition of a binary solution into an inhomogeneous phase

ABSTRACT In the framework of the theoretical model of the phase transition of binary solutions into spatially inhomogeneous states proposed earlier by the authors [Poluektov Y, Soroka AA. Transition of a binary solution into an inhomogeneous phase. Phase Transition. 2022;95:267–280], which takes into account nonlinear effects, the role of the cubic in concentration term in the expansion of free energy was studied. It is shown that taking into account the cubic term contributes to the stabilization of a homogeneous state. The existence of two inhomogeneous phases in an isotropic medium, considered in [Poluektov Y, Soroka AA. Transition of a binary solution into an inhomogeneous phase. Phase Transition. 2022;95:267–280], proves to be possible only at half the concentration of the solution. The contribution of inhomogeneity effects to thermodynamic quantities is calculated. Phase transitions from a homogeneous state and between inhomogeneous phases are second-order phase transitions.

A dynamic phase separation model for glass transition behavior in water-triggered shape memory polymer towards programmable recovery onset

Water-triggered shape memory polymers (SMPs) have been extensively studied for biomedical applications due to their advantages of non-thermal actuation capability. However, few studies have been carried out to explore the working principle of shape recovery onset, which is essentially determined by the complex reactions between polymer macromolecules and water molecules. In this study, we developed a phase separation model to describe the dynamic glass transition in water-triggered SMPs. Based on the phase transition theory, dense and dilute phase separations of polymer macromolecules can be achieved when the dynamic diffusions of water molecules in the SMPs undergo dehydration and absorption processes, respectively. Then, the dynamic glass transition is resulted from the dehydration and absorption of water molecules, leading to the dense and dilute phases in the SMPs. Therefore, a free-energy equation has been developed to characterize the recovery onset, in which the mixing free energy and elastic free energy are originated from the Flory–Huggins solution theory and phase separation model, respectively. Moreover, the glass transition and its connection to shape recovery behaviors, i.e. recovery ratio, relaxation time and dynamic mechanical modulus, have also been investigated, according to the Fick’s diffusion law. Meanwhile, onset of programmable recovery has been explained by the dynamic phase separation, based on the transpiration theory and permeability model. Finally, the proposed model is verified using the experimental results reported in the literature. This study is expected to provide a fundamental approach to formulate the constitutive relationship between the dynamic phase separation and programmable recovery onset in the water-triggered SMPs.

Theoretical and experimental study of strain localization phenomenon based on phase transition theory

In the study of large-scale localized strain features, localized strain can lead to energy release and seismic effects. From the macroscopic process of localized strain, it is found that localized deformation is accompanied by structural weakening, which is due to phase changes in rocks. The phase change corresponds to the secondary phase transition process in physics. The present study illustrates this phenomenon from the perspective of secondary phase transition theory in statistical physics, combining the localized strain features on a large scale. Theoretical analysis and experimental studies were carried out using three brittle rocks, including marble, granite and red sandstone. First, two perturbation methods, i.e., Krylov–Bogoliubov method and Poincare method, are used to calculate the higher-order control equations in analytical model. The influences of control equation coefficients on the strain localization process are analyzed. Then the uniaxial compression tests are carried out on the three rocks to record the strain process. Finally, the theoretical and experimental results are compared to analyze the strain localization phenomenon. The comparison results show that both the Krylov–Bogoliubov solution and the Poincare solution in the analytical model can well describe the evolution characteristics of localized strain. It indicates that the theoretical model is valid and has high accuracy. The Poincare method better simulates the nonlinear phenomenon of strain localization. The present study provides a new theoretical method to better understand the strain localization phenomenon.

Scaling theory of fractal complex networks

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes with which we cover the network when determining its box dimension. This approach—grounded in both scaling theory of phase transitions and renormalization group theory—leads to the consistent scaling theory of fractal complex networks, which complements the collection of scaling exponents with several new ones and reveals various relationships between them. We propose the introduction of two classes of exponents: microscopic and macroscopic, characterizing the local structure of fractal complex networks and their global properties, respectively. Interestingly, exponents from both classes are related to each other and only a few of them (three out of seven) are independent, thus bridging the local self-similarity and global scale-invariance in fractal networks. We successfully verify our findings in real networks situated in various fields (information—the World Wide Web, biological—the human brain, and social—scientific collaboration networks) and in several fractal network models.

Statistical mechanics of phenotypic eco-evolution: From adaptive dynamics to complex diversification

The ecological and evolutionary dynamics of large populations can be addressed theoretically using concepts and methodologies from statistical mechanics. This approach has been extensively discussed in the literature, both within the realm of population genetics, which focuses on genes or “genotypes,” and in adaptive dynamics, which emphasizes traits or “phenotypes.” Following this tradition, here we construct a theoretical framework allowing us to derive “macroscopic” evolutionary equations from a general “microscopic” stochastic dynamics representing the fundamental processes of reproduction, mutation, and selection in a large community of individuals, each one characterized by its phenotypic features. Importantly, in our setup, ecological and evolutionary timescales are intertwined, which makes it particularly suitable to describe microbial communities, a timely topic of utmost relevance. The framework leads to a probabilistic description—even in the case of arbitrarily large populations—of the distribution of individuals in phenotypic space as encoded in what we call the “generalized Crow-Kimura equation” or “generalized replicator-mutator equation.” We discuss the limits in which such an equation reduces to the (deterministic) theory of “adaptive dynamics,” i.e., the standard approach to evolutionary dynamics in phenotypic space. Moreover, we emphasize the aspects of the theory that are beyond the reach of standard adaptive dynamics. In particular, by developing a simple model of a growing and competing population as an illustrative example, we demonstrate that the resulting probability distribution can undergo “dynamical phase transitions.” These transitions may involve shifts from a unimodal distribution to a bimodal distribution, generated by an evolutionary branching event, or to a multimodal distribution through a cascade of evolutionary branching events. Furthermore, our formalism allows us to rationalize these cascades using the parsimonious approach of Landau's theory of phase transitions. Finally, we extend the theory to account for finite populations and illustrate the possible consequences of the resulting stochastic or “demographic” effects. Altogether, the present framework extends and/or complements existing approaches to evolutionary and adaptive dynamics and paves the way to more systematic studies of microbial communities as well as to future developments including theoretical analyses of the evolutionary process from the general perspective of nonequilibrium statistical mechanics. Published by the American Physical Society 2024