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The earlier times of the evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices built from different time evolutions of a simple testbed spin system, as the spin-1/2 and spin-1 Ising models, we analyzed the density of eigenvalues for different temperatures of the so called Wishart matrices. We observe a transition in the shape of the distribution that presents a gap of eigenvalues for temperatures lower than the critical temperature, or in its roundness, with a continuous migration to the Marchenko–Pastur law in the paramagnetic phase. We consider the analysis a promising method to be applied in other spin systems, with or without defined Hamiltonian, to characterize phase transitions. Our approach differs from the alternatives in literature since it uses the concept of magnetization matrix, not the spatial matrix of single spins. [ABSTRACT FROM AUTHOR]

Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at a given transition rate. This paper explores how such stochastic processes involving multiple particles can model group behaviors of ants. Recent experimental research by the last author's group has investigated how ants switch between two types of primarily relied cues to select foraging paths based on the current situation. Here, we propose a discrete-time interacting random walk model on a square lattice, incorporating two types of hopping rules. Numerical simulation results demonstrate global changes in selected homing paths, transitioning from trailing paths of the 'pheromone road' to nearly optimal paths depending on the switching parameters. By introducing two types of order parameters characterizing the dependence of homing duration distributions on switching parameters, we discuss these global changes as phase transitions in ant path selections. We also study critical phenomena associated with continuous phase transitions. [ABSTRACT FROM AUTHOR]

Attention in the literature has increasingly turned to the issue of the dependence on ensemble and boundary conditions of fluctuation-induced forces. We have recently investigated this problem in the one-dimensional Ising model with periodic and antiperiodic boundary conditions (Annals of Physics 4 59, 169533 (2023)). Significant variations of the behavior of Casimir and Helmholtz forces was observed, depending on both ensemble and boundary conditions. Here we extend our study by considering the problem in the important case of Dirichlet (also termed free, or missing neighbors) boundary conditions. The advantage of the mathematical formulation of the problem in terms of Chebyshev polynomials is demonstrated and, in this approach, expressions for the partition functions in the canonical and the grand canonical ensembles are presented. We prove analytically that the Casimir force is attractive for all values of temperature and external ordering field, while the Helmholtz force can be both attractive and repulsive. [ABSTRACT FROM AUTHOR]

The layered van der Waals material ZrTe 5 is known as a candidate topological insulator (TI), however its topological phase and the relation with other properties such as an apparent Dirac semimetallic state is still a subject of debate. We employ a semiclassical multicarrier transport (MCT) model to analyze the magnetotransport of ZrTe 5 nanodevices at hydrostatic pressures up to 2 GPa. The temperature dependence of the MCT results between 10 and 300 K is assessed in the context of thermal activation, and we obtain the positions of conduction and valence band edges in the vicinity of the chemical potential. We find evidence of the closing and re-opening of the band gap with increasing pressure, which is consistent with a phase transition from weak to strong TI. This matches expectations from ab initio band structure calculations, as well as previous observations that CVT-grown ZrTe 5 is a weak TI in ambient conditions., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2024.)

The nature of particle and entropy flow between two superfluids is often understood in terms of reversible flow carried by an entropy-free, macroscopic wavefunction. While this wavefunction is responsible for many intriguing properties of superfluids and superconductors, its interplay with excitations in non-equilibrium situations is less understood. Here we observe large concurrent flows of both particles and entropy through a ballistic channel connecting two strongly interacting fermionic superfluids. Both currents respond nonlinearly to chemical potential and temperature biases. We find that the entropy transported per particle is much larger than the prediction of superfluid hydrodynamics in the linear regime and largely independent of changes in the channel's geometry. By contrast, the timescales of advective and diffusive entropy transport vary significantly with the channel geometry. In our setting, superfluidity counterintuitively increases the speed of entropy transport. Moreover, we develop a phenomenological model describing the nonlinear dynamics within the framework of generalized gradient dynamics. Our approach for measuring entropy currents may help elucidate mechanisms of heat transfer in superfluids and superconducting devices., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2024.)

Highlights • The dynamic (complex) dipolar and quadrupolar susceptibilities are obtained. • Temperature, crystal-field and frequency variations of susceptibilities are examined. • There are broad peaks in the quadrupolar dispersion and absorption factors. • These maxima reflect the very strong quadrupolar fluctuations at a critical point. Abstract The expressions for dynamic (complex) dipolar and quadrupolar susceptibilities are obtained within the framework of the linear theory of irreversible thermodynamics in the Blume-Emery-Griffiths model. Frequency, temperature as well as crystal field dependences of the dispersion relations and absorption factors are investigated for two different phase diagram topologies which take place for K/J = 3 and K/J = 5.0. Their behaviors near the second- and first-order transition points as well as multi-critical points such as tricritical, triple and critical endpoint are presented. [ABSTRACT FROM AUTHOR]

A simple method to estimate percolation thresholds p c in lattice models is presented. The technique is based on the calculation of the probabilities R L X (p) for finding a percolating cluster of type X [ X could be horizontal (H), vertical (V), average (A), intersection (I), or union (U)] on a finite lattice of side length L at concentration p of occupied sites. The functions R L X (p) are obtained by numerical simulations. Then, (1) effective percolation thresholds p c X , r (L) are estimated from the condition R L X (p) = r (where r is a parameter ranging between 0 and 1); and (2) the percolation threshold in the thermodynamic limit is determined by extrapolating the effective percolation thresholds to infinite L. The methodology presented herein contains and extends the classical scheme developed by Yonezawa, Sakamoto and Hori, offering a more complete and versatile theoretical/simulation framework to calculate percolation thresholds. The approach is validated by successfully comparing with well-known results obtained for the problem of random site percolation on square lattices. Taking advantage of the behavior of the curves of p c X , r (L) for different values of the parameter r , more general scaling relations are proposed for the effective percolation thresholds. Finally, the technique is applied to model experimental data of clogging transitions in a two-dimensional silo with a vibrated base. • A new procedure to calculate percolation thresholds in lattice systems is presented. • Multiple effective thresholds are obtained from the percolation probability functions. • The method is applied to the problem of random site percolation on square lattices. • The obtained results are in good agreement with previous calculations in literature. • The clogging transition in a 2D silo is discussed in terms of percolation theory. [ABSTRACT FROM AUTHOR]