Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

We consider a one-dimensional system of interacting particles (which can be atoms, molecules, ions, etc.), in which particles are subjected to a bistable potential the double-well shape of which is tunable via a shape deformability parameter. Our objective is to examine the impact of shape deformability on the order of transition in quantum tunneling in the bistable system, and on the possible existence of exact solutions to the transfer-integral operator associated with the partition function of the system. The bistable potential is represented by a class composed of three families of parametrized double-well potentials, whose minima and barrier height can be tuned distinctly. It is found that the extra degree of freedom, introduced by the shape deformability parameter, favors a first-order transition in quantum tunneling, in addition to the second-order transition predicted with the $$\phi ^4$$ ϕ 4 model. This first-order transition in quantum tunneling, which is consistent with Chudnovsky’s conjecture of the influence of the shape of the potential barrier on the order of thermally assisted transitions in bistable systems, is shown to occur at a critical value of the shape-deformability parameter which is the same for the three families of parametrized double-well potentials. Concerning the statistical mechanics of the system, the associate partition function is mapped onto a spectral problem by means of the transfer-integral formalism. The condition that the partition function can be exactly integrable, is determined by a criterion enabling exact eigenvalues and eigenfunctions for the transfer-integral operator. Analytical expressions of some of these exact eigenvalues and eigenfunctions are given, and the corresponding ground-state wavefunctions are used to compute the probability density which is relevant for calculations of thermodynamic quantities such as the correlation functions and the correlation lengths. Graphic Abstract

Heisenberg spins on an anisotropic triangular lattice: PdCrO2 under uniaxial stress

When Heisenberg spins interact antiferromagnetically on a triangular lattice and nearest-neighbor interactions dominate, the ground state is 120◦ antiferromagnetism. In this work, we probe the response of this state to lifting the triangular symmetry, through investigation of the triangular antiferromagnet PdCrO2 under uniaxial stress by neutron diffraction and resistivity measurements. The periodicity of the magnetic order is found to change rapidly with applied stress; the rate of change indicates that the magnetic anisotropy is roughly forty times the stress-induced bond length anisotropy. At low stress, the incommensuration period becomes extremely long, on the order of 1000 lattice spacings; no locking of the magnetism to commensurate periodicity is detected. Separately, the magnetic structure is found to undergo a first-order transition at a compressive stress of ∼0.4 GPa, at which the interlayer ordering switches from a double- to a single-q structure.

Linear-superelastic Ti-Nb nanocomposite alloys with ultralow modulus via high-throughput phase-field design and machine learning

The optimal design of shape memory alloys (SMAs) with specific properties is crucial for the innovative application in advanced technologies. Herein, inspired by the recently proposed design concept of concentration modulation, we explore martensitic transformation (MT) in and design the mechanical properties of Ti-Nb nanocomposites by combining high-throughput phase-field simulations and machine learning (ML) approaches. Systematic phase-field simulations generate data of the mechanical properties for various nanocomposites constructed by four macroscopic degrees of freedom. An ML-assisted strategy is adopted to perform multiobjective optimization of the mechanical properties, through which promising nanocomposite configurations are prescreened for the next set of phase-field simulations. The ML-guided simulations discover an optimized nanocomposite, composed of Nb-rich matrix and Nb-lean nanofillers, that exhibits a combination of mechanical properties, including ultralow modulus, linear super-elasticity, and near-hysteresis-free in a loading-unloading cycle. The exceptional mechanical properties in the nanocomposite originate from optimized continuous MT rather than a sharp first-order transition, which is common in typical SMAs. This work demonstrates the great potential of ML-guided phase-field simulations in the design of advanced materials with extraordinary properties.

Emergence of order in condensates composed of multi-valent, multi-domain proteins

Many RNA-binding proteins (RBPs) that assemble into membraneless organelles, have a common architecture including disordered prion-like domain (PLD) and folded RNA-binding domain (RBD). An enrichment of PLD within the condensed phase gives rise to formation, on longer time scales, amyloid-like fibrils (aging). In this study, we employ coarse-grained Langevin dynamics simulations to explore the physical basis for the structural diversity in condensed phases of multi-domain RBPs. We discovered a highly cooperative first order transition between disordered (liquid-like) structures and an ordered (solid-like) phase whereby chains of PLD organize in fibrils with high nematic orientational order. Cooperativity of this liquid-solid transition makes fibril formation highly malleable to mutations or post-translational modifications. An interplay between homo-domain (PLD-PLD) and hetero-domain (PLD-RBD) interactions results in variety of structures with distinct spatial architectures. Our results provide a mechanistic understanding of how multi-domain RBPs could form assemblies with distinct structural and, potentially, material properties.

First-order antiferromagnetic transitions of SrMn2P2 and CaMn2P2 single crystals containing corrugated-honeycomb Mn sublattices

SrMn2P2 and CaMn2P2 are insulators that adopt the trigonal CaAl2Si2-type structure containing corrugated Mn honeycomb layers. Magnetic susceptibility χ and heat capacity versus temperature T data reveal a weak first-order antiferromagnetic (AFM) transition at the Néel temperature TN=53(1) K for SrMn2P2 and a strong first-order AFM transition at TN=69.8(3) K for CaMn2P2. Both compounds exhibit isotropic and nearly T-independent χ(T≤TN), suggesting magnetic structures in which nearest-neighbor moments are aligned at ≈120° to each other. The 31P NMR measurements confirm the strong first-order transition in CaMn2P2 but show critical slowing down above TN for SrMn2P2, thus also evidencing second-order character. The 31P NMR measurements indicate that the AFM structure of CaMn2P2 is commensurate with the lattice whereas that of SrMn2P2 is incommensurate. These first-order AFM transitions are unique among the class of (Ca, Sr, Ba)Mn2 (P, As, Sb, Bi)2 compounds that otherwise exhibit second-order AFM transitions. This result challenges our understanding of the circumstances under which first-order AFM transitions occur.

Gliding Down the QCD Transition Line, from Nf = 2 till the Onset of Conformality

We review the hot QCD transition with varying number of flavours, from two till the onset of the conformal window. We discuss the universality class for Nf=2, along the critical line for two massless light flavours, and a third flavour whose mass serves as an interpolator between Nf=2 and Nf=3. We identify a possible scaling window for the 3D O(4) universality class transition, and its crossover to a mean field behaviour. We follow the transition from Nf=3 to larger Nf, when it remains of first order, with an increasing coupling strength; we summarise its known properties, including possible cosmological applications as a model for a strong electroweak transition. The first order transition, and its accompanying second order endpoint, finally morphs into the essential singularity at the onset of the conformal window, following the singular behaviour predicted by the functional renormalisation group.

Modular coinduction up-to for higher-order languages via first-order transition systems

The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible functions. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the pi-calculus, the lambda-calculus, and a (call-by-value) lambda-calculus with references.

Is there supersymmetric Lee–Yang fixed point in three dimensions?

The supersymmetric Lee–Yang model is arguably the simplest interacting supersymmetric field theory in two dimensions, albeit nonunitary. A natural question is if there is an analogue of supersymmetric Lee–Yang fixed point in higher dimensions. The absence of any [Formula: see text] symmetry (except for fermion numbers) makes it impossible to approach it by using perturbative [Formula: see text] expansions. We find that the truncated conformal bootstrap suggests that candidate fixed points obtained by the dimensional continuation from two dimensions annihilate below three dimensions, implying that there is no supersymmetric Lee–Yang fixed point in three dimensions. We conjecture that the corresponding phase transition, if any, will be the first-order transition.

The Effect of Topology on Phase Behavior under Confinement

This work studies how morphology (i.e., the shape of a structure) and topology (i.e., how different structures are connected) influence wall adsorption and capillary condensation under tight confinement. Numerical simulations based on classical density functional theory (cDFT) are run for a wide variety of geometries using both hard-sphere and Lennard-Jones fluids. These cDFT computations are compared to results obtained using the Minkowski functionals. It is found that the Minkowski functionals can provide a good description of the behavior of Lennard-Jones fluids down to small system sizes. In addition, through decomposition of the free energy, the Minkowski functionals provide a good framework to better understand what are the dominant contributions to the phase behavior of a system. Lastly, while studying the phase envelope shift as a function of the Minkowski functionals it is found that topology has a different effect depending on whether the phase transition under consideration is a continuous or a discrete (first-order) transition.

EEGs Disclose Significant Brain Activity Correlated with Synaptic Fickleness

We here study a network of synaptic relations mingling excitatory and inhibitory neuron nodes that displays oscillations quite similar to electroencephalogram (EEG) brain waves, and identify abrupt variations brought about by swift synaptic mediations. We thus conclude that corresponding changes in EEG series surely come from the slowdown of the activity in neuron populations due to synaptic restrictions. The latter happens to generate an imbalance between excitation and inhibition causing a quick explosive increase of excitatory activity, which turns out to be a (first-order) transition among dynamic mental phases. Moreover, near this phase transition, our model system exhibits waves with a strong component in the so-called delta-theta domain that coexist with fast oscillations. These findings provide a simple explanation for the observed delta-gamma and theta-gamma modulation in actual brains, and open a serious and versatile path to understand deeply large amounts of apparently erratic, easily accessible brain data.