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A central tenant in the classification of phases is that boundary conditions cannot affect the bulk properties of a system. In this work, we show striking, yet puzzling, evidence of a clear violation of this assumption. We use the prototypical example of an XYZ chain with no external field in a ring geometry with an odd number of sites and both ferromagnetic and antiferromagnetic interactions. In such a setting, even at finite sizes, we are able to calculate directly the spontaneous magnetizations that are traditionally used as order parameters to characterize the system's phases. When ferromagnetic interactions dominate, we recover magnetizations that in the thermodynamic limit lose any knowledge about the boundary conditions and are in complete agreement with standard expectations. On the contrary, when the system is governed by antiferromagnetic interactions, the magnetizations decay algebraically to zero with the system size and are not staggered, despite the antiferromagnetic coupling. We term this behavior ferromagnetic mesoscopic magnetization. Hence, in the antiferromagnetic regime, our results show an unexpected dependence of a local, one-spin expectation values on the boundary conditions, which is in contrast with predictions from the general theory.

SignificanceSr2RuO4 is distinctive among unconventional superconductors, in that in addition to exhibiting evidence for strong correlations, it is stoichiometric and extremely clean. As a result, its electronic structure is unusually well characterized, rendering it an ideal platform for developing a deep understanding of the mechanism behind the emergence of the superconducting state from a Fermi liquid. Toward that end, an unambiguous determination of the pairing symmetry is an essential step. For more than 2 decades, the preponderance of evidence pointed to a triplet spin pairing state and only recently has this interpretation been challenged. By field-dependent NMR Knight shift measurements, we eliminate from further consideration all candidate purely odd-parity triplet pairing states. Unambiguous identification of the superconducting order parameter symmetry in Sr2RuO4 has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

It has been well established that the origin of p -wave superconductivity is the balance between pair creation and annihilation, described by the spin-less fermionic Kitaev chain model. In this work, we study the dynamics of a composite system where the pair source and drain are spatially separated by a long distance. We show that this non-Hermitian system possesses a high-order exceptional point (EP) when only a source or drain is considered. The EP dynamics provide a clear picture: A pair source can fully fill the system with pairs, while a drain can completely empty the system. When the two coexist simultaneously, the dynamics depend on the distance and the relative phase between the pair creation and annihilation terms. Analytical analysis and numerical simulation results show that the superconducting state can be dynamically established at the resonant pair source and drain: from an initial empty state to a stationary state with the maximal pair order parameter. It provides an alternative way of understanding the mechanism of the nonequilibrium superconducting state.

The dynamic magnetic and thermodynamic behaviors of the mixed-spin (1/2, 1, 3/2) Ising edge-modified graphene-like nanoparticles in a time-dependent magnetic field are studied by Monte Carlo simulation. The influence of temperature, exchange coupling, crystal field, and time-dependent magnetic field on the dynamic order parameter, magnetic susceptibility, and internal energy are investigated. The simulations reveal that the compensation behavior of the system occurs in a certain parameter range. Strong crystal field and weak exchange coupling promote the compensation behavior in the system, while increasing the amplitude of the oscillating magnetic field reduces the compensation temperature. Furthermore, the system shows the interesting multiple dynamic hysteresis behaviors under the influence of different parameters.

This paper investigates the problem of parameter estimation for fractional-order linear systems when output signal is polluted by noise and outliers. Different from conventional filtering and semi-definite programming methods, the outliers detection problem is formulated as a matrix decomposition problem based on a novel nuclear norm method, which can not only make exact detection of outliers, but also estimate measurement noise at the same time. Then, a new parameter estimation approach is developed via a modified fractional-order gradient method with variable initial value mechanism and fractional-order parameter update law. With the adoption of recovered output signal, the proposed approach can obtain much better estimation performance, whose effectiveness and superiority are verified by strict mathematical analysis and detailed numerical examples.

Cells cooperate as groups to achieve structure and function at the tissue level, during which specific material characteristics emerge. Analogous to phase transitions in classical physics, transformations in the material characteristics of multicellular assemblies are essential for a variety of vital processes including morphogenesis, wound healing, and cancer. In this work, we develop configurational fingerprints of particulate and multicellular assemblies and extract volumetric and shear order parameters based on this fingerprint to quantify the system disorder. Theoretically, these two parameters form a complete and unique pair of signatures for the structural disorder of a multicellular system. The evolution of these two order parameters offers a robust and experimentally accessible way to map the phase transitions in expanding cell monolayers and during embryogenesis and invasion of epithelial spheroids.

We propose an extended Bogoliubov transformation in real space for spinless fermions, based on which a class of Kitaev chains of length 2 N with zero chemical potential can be mapped to two independent Kitaev chains of length N . It provides an alternative way to investigate a complicated system from the result of relatively simple systems. We demonstrate the implications of this decomposition by a Su–Schrieffer–Heeger Kitaev model, which supports rich quantum phases. The features of the system, including the groundstate topology and nonequilibrium dynamics, can be revealed directly from that of sub-Kitaev chains. Based on this connection, two types of Bardeen–Cooper–Schrieffer (BCS)-pair order parameters are introduced to characterize the phase diagram, showing the ingredient of two different BCS pairing modes. Analytical analysis and numerical simulations show that the real-space decomposition for the ground state still holds true approximately in presence of finite chemical potential in the gapful regions.

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

We propose a family of order parameters to detect the symmetry fractionalization class of anyons in 2D topological phases. This fractionalization class accounts for the projective, as opposed to linear, representations of the symmetry group on the anyons. We focus on quantum double models on a lattice enriched with an internal symmetry in the framework of G-isometric projected entangled pair states. Unlike previous schemes based on reductions to effective 1D systems (dimensional compactification), the order parameters presented here can be probed on genuinely two-dimensional geometries, and are local: they rely on operations on few neighbouring particles in the bulk. The power of these order parameters is illustrated with several combinations of topological content and symmetry. We demonstrate that a strictly finer phase distinction than that provided by dimensional compactification can be obtained. As particular examples, the resolution power of these order parameters is illustrated for a case with non-abelian topological order, and for another with symmetries that involves permutation of anyons.

Recently, Baldwin and Swingle (J Stat Phys 190(7):125, 2023) considered spin glass models with additional conventional order parameters characterizing single-replica properties. These parameters are distinct from the standard order parameter, the overlap, used to measure correlations between replicas. A “min-max” formula for the free energy was prescribed in Baldwin and Swingle (2023). We rigorously verify this prescription in the setting of vector spin glass models featuring additional deterministic spin interactions. Notably, our results can be viewed as a generalization of the Parisi formula for vector spin glass models in Panchenko (Ann Probab 46(2):865–896, 2018), where the order parameter for self-overlap is already present.