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In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially defined by a regular square lattice and with probability $p$ each site is tested for the possibility of creating a long-range interaction with any other site that has not yet received one. Here, we used the specific case where $p=1$, meaning that every site in the network has one long-range interaction in addition to the short-range interactions of the regular lattice. These long-range interactions depend on a power-law form, $J_{ij}=r_{ij}^{-\alpha}$, with the geometric distance $r_{ij}$ between connected sites $i$ and $j$. In current two-dimensional model, we found that mean-field critical behavior is observed only at $\alpha=0$. As $\alpha$ increases, the network size influences the phase transition point of the system, i.e., indicating a crossover behavior. However, given the two-dimensional system, we found the critical behavior of the short-range interaction at $\alpha\approx2$. Thus, the limitation in the number of long-range interactions compared to the globally coupled model, as well as the form of the decay of these interactions, prevented us from finding a regime with finite phase transition points and continuously varying critical exponents in $0<\alpha<2$., Comment: 7 pages, 8 figures, 2 tables

Meta-stable states are identified in the Ising model with competition between the Glauber and Kawasaki dynamics. The model of interaction between magnetic moments was implemented on a network where the degree distribution follows a power-law of the form, $P(k)\sim k^{-\alpha}$. The evolution towards the stationary state occurred through the competition between two dynamics, driving the system out of equilibrium. In this competition, with probability $q$, the system was simulated in contact with a heat bath at temperature $T$ by the Glauber dynamics, while with probability $1-q$, the system experienced an external energy influx governed by the Kawasaki dynamics. The phase diagrams of $T$ versus $q$ were obtained, which are dependent on the initial state of the system, and exhibit first- and second-order phase transitions. In all diagrams, for intermediate values of $T$, the phenomenon of self-organization between the ordered phases was observed. In the regions of second-order phase transitions, we have verified the universality class of the system through the critical exponents of the order parameter $\beta$, susceptibility $\gamma$, and correlation length $\nu$. Furthermore, in the regions of first-order phase transitions, we have demonstrated the instability due to transitions between the ordered phases through hysteresis-like curves of the order parameter, in addition to the existence of absorbing states. We also estimated the value of the tricritical points when the discontinuity in the order parameter in the phase transitions was no longer observed., Comment: 12 pages and 10 figures

Monochromatic gamma-ray signals constitute a potential smoking gun signature for annihilating or decaying dark matter particles that could relatively easily be distinguished from astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre region as well as of selected dwarf spheroidal galaxies. We find that current limits and detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard for gamma-ray astronomy also in this respect, as the world's largest and most sensitive high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV energies and the adopted observational strategy focussing on regions with large dark matter densities. Throughout our analysis, we use up-to-date instrument response functions, and we thoroughly model the effect of instrumental systematic uncertainties in our statistical treatment. We further present results for other potential signatures with sharp spectral features, e.g.~box-shaped spectra, that would likewise very clearly point to a particle dark matter origin., Comment: 44 pages JCAP style (excluding author list and references), 19 figures; minor changes to match published version

Galaxy clusters are expected to be dark matter (DM) reservoirs and storage rooms for the cosmic-ray protons (CRp) that accumulate along the cluster's formation history. Accordingly, they are excellent targets to search for signals of DM annihilation and decay at gamma-ray energies and are predicted to be sources of large-scale gamma-ray emission due to hadronic interactions in the intracluster medium. We estimate the sensitivity of the Cherenkov Telescope Array (CTA) to detect diffuse gamma-ray emission from the Perseus galaxy cluster. We perform a detailed spatial and spectral modelling of the expected signal for the DM and the CRp components. For each, we compute the expected CTA sensitivity. The observing strategy of Perseus is also discussed. In the absence of a diffuse signal (non-detection), CTA should constrain the CRp to thermal energy ratio within the radius $R_{500}$ down to about $X_{500}<3\times 10^{-3}$, for a spatial CRp distribution that follows the thermal gas and a CRp spectral index $\alpha_{\rm CRp}=2.3$. Under the optimistic assumption of a pure hadronic origin of the Perseus radio mini-halo and depending on the assumed magnetic field profile, CTA should measure $\alpha_{\rm CRp}$ down to about $\Delta\alpha_{\rm CRp}\simeq 0.1$ and the CRp spatial distribution with 10% precision. Regarding DM, CTA should improve the current ground-based gamma-ray DM limits from clusters observations on the velocity-averaged annihilation cross-section by a factor of up to $\sim 5$, depending on the modelling of DM halo substructure. In the case of decay of DM particles, CTA will explore a new region of the parameter space, reaching models with $\tau_{\chi}>10^{27}$s for DM masses above 1 TeV. These constraints will provide unprecedented sensitivity to the physics of both CRp acceleration and transport at cluster scale and to TeV DM particle models, especially in the decay scenario., Comment: 93 pages (including author list, appendix and references), 143 figures. Submitted to JCAP

The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability $q$ in which the one-spin flip process simulate the contact with a heat bath at a given temperature $T$, and with a probability ($1-q$) the two-spin flip process mimics the system subjected to an external flux of energy into it. The system network is described by a power-law degree distribution in the form $P(k)\sim k^{-\alpha}$, and the restriction is made by fixing the maximum, $k_{m}$, and minimum, $k_{0}$, degree on distribution for the whole network size. This restriction keeps finite the second and fourth moment of degree distribution, allowing us to obtain a finite critical point for any value of $\alpha$. For these critical points, we have calculated the thermodynamic quantities of the system, such as, the total ${m}_{N}^{F}$ and staggered ${m}_{N}^{AF}$ magnetizations per spin, susceptibility $\chi_{N}$, and reduced fourth-order Binder cumulant ${U}_{N}$, for several values of lattice size $N$ and exponent $1\le\alpha\le5$. Therefore, the phase diagram was built and a self-organization phenomena is observed from the transitions between antiferromagnetic AF to paramagnetic P, and P to ferromagnetic F phases. Using the finite-size scaling theory, we also obtained the critical exponents for the system, and a mean-field critical behavior is observed, exhibiting the same universality class of the system on the equilibrium and out of it., Comment: 9 pages, 6 figures and 2 tables

We have studied the mixed spin-1/2 and 1 Ising ferrimagnetic system with a random anisotropy on a triangular lattice with three interpenetrating sublattices $A$, $B$, and $C$. The spins on the sublattices are represented by $\sigma_{A}$ (states $\pm1/2$), $\sigma_{B}$ (states $\pm1/2$), and $S_{C}$ (states $\pm1$, $0$). We have performed Monte Carlo simulations to obtain the phase diagram temperature $k_{\text{B}}T/\left|J\right|$ versus the strength of the random anisotropy $D/\left|J\right|$. The phase boundary between two ferrimagnetic $FR_{1}$ and $FR_{2}$ phases at lower temperatures are always first-order for $p<0.25$ and second-order phase transition between the $FR_{1}$, $FR_{2}$ and the paramagnetic $P$ phases. On the other hand, for values of $p\gtrapprox0.5$, the phase diagram presents only second-order phase transition lines., Comment: 10 pages, 7 figures

The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because independently of the network size, we always have fixed the maximum $k_{m}$ and a minimum $k_{0}$ degree on distribution, being that for it, we only limit the minimum network size of the system. We calculated the thermodynamic quantities of the system, such as, the magnetization per spin $\textrm{m}_{\textrm{L}}$, the magnetic susceptibility $\chi_{\textrm{L}}$, and the reduced fourth-order Binder cumulant $\textrm{U}_{\textrm{L}}$, as a function of temperature $T$ for several values of lattice size $N$ and exponent $1\le\alpha\le5$. For the values of $\alpha$, we have obtained the finite critical points due to we also have finite second and fourth moments in the degree distribution, and the phase diagram was constructed for the equilibrium states of the model in the plane $T$ versus $k_{0}$, $k_{m}$, and $\alpha$, showing a transition between the ferromagnetic $F$ to paramagnetic $P$ phases. Using the finite-size scaling (FSS) theory, we also have obtained the critical exponents for the system, and a mean-field critical behavior is observed., Comment: 9 pages, 8 figures and 2 tables

We call an algebra $A$ commutator-simple if $[A,A]$ does not contain nonzero ideals of $A$. After providing several examples, we show that in these algebras derivations are determined by a condition that is applicable to the study of local derivations. This enables us to prove that every continuous local derivation $D\colon L^1(G)\to L^1(G)$, where $G$ is a unimodular locally compact group, is a derivation. We also give some remarks on homomorphism-like maps in commutator-simple algebras.

In this work, we have studied the Ising model with one- and two-spin flip competing dynamics on a two-dimensional additive small-world network (A-SWN). The system model consists of a $L\times L$ square lattice where each site of the lattice is occupied by a spin variable that interacts with the nearest neighbor spins and it has a certain probability $p$ of being additionally connected at random to one of its farther neighbors. The dynamics present in the system can be defined by the probability $q$ of being in contact with a heat bath at a given temperature $T$ and, at the same time, with a probability of $1-q$ the system is subjected to an external flux of energy into the system. The contact with the heat bath is simulated by one-spin flip according to the Metropolis prescription, while the input of energy is mimicked by the two-spin flip process, involving a simultaneous flipping of a pair of neighboring spins. We have employed Monte Carlo simulations to obtain the thermodynamic quantities of the system, such as, the total $\textrm{m}_{\textrm{L}}^{\textrm{F}}$ and staggered $\textrm{m}_{\textrm{L}}^{\textrm{AF}}$ magnetizations per spin, the susceptibility $\chi_{\textrm{L}}$, and the reduced fourth-order Binder cumulant $\textrm{U}_{\textrm{L}}$. We have built the phase diagram for the stationary states of the model in the plane $T$ versus $q$, showing the existence of two continuous transition lines for each value of $p$: one line between the ferromagnetic $F$ and paramagnetic $P$ phases, and the other line between the $P$ and antiferromagnetic $AF$ phases. Therefore, we have shown that the phase diagram topology changes when $p$ increases. Using the finite-size scaling analysis, we also obtained the critical exponents for the system, where varying the parameter $p$, we have observed a different universality class from the Ising model in the regular square lattice to the A-SWN., Comment: 11 pages, 9 figures and 4 tables. arXiv admin note: text overlap with arXiv:2206.04202

In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a spin variable that interacts with the nearest neighbor and has a certain probability p of being additionally connected at random to one of its farther neighbors. The system is in contact with a heat bath at a given temperature T and it is simulated by one-spin flip according to the Metropolis prescription. We have calculated the thermodynamic quantities of the system, such as, the magnetization per spin m, magnetic susceptibility chi, and the reduced fourth-order Binder cumulant U as a function of T for several values of lattice size L and additive probability p. We also have constructed the phase diagram for the equilibrium states of the model in the plane T versus p showing the existence of a continuous transition line between the ferromagnetic F and paramagnetic P phases. Using the finite-size scaling (FSS) theory, we have obtained the critical exponents for the system, where varying the parameter p, we have observed a change in the critical behavior from the regular square lattice Ising model to A-SWN., Comment: 8 pages, 8 figures and 2 tables

The physics motivation and the conceptual design of the PIONEER experiment, a next-generation rare pion decay experiment testing lepton flavor universality and CKM unitarity, are described. Phase I of the PIONEER experiment, which was proposed and approved at Paul Scherrer Institut, aims at measuring the charged-pion branching ratio to electrons vs.\ muons, $R_{e/\mu}$, 15 times more precisely than the current experimental result, reaching the precision of the Standard Model (SM) prediction at 1 part in $10^4$. Considering several inconsistencies between the SM predictions and data pointing towards the potential violation of lepton flavor universality, the PIONEER experiment will probe non-SM explanations of these anomalies through sensitivity to quantum effects of new particles up to the PeV mass scale. The later phases of the PIONEER experiment aim at improving the experimental precision of the branching ratio of pion beta decay (BRPB), $\pi^+\to \pi^0 e^+ \nu (\gamma)$, currently at $1.036(6)\times10^{-8}$, by a factor of three (Phase II) and an order of magnitude (Phase III). Such precise measurements of BRPB will allow for tests of CKM unitarity in light of the Cabibbo Angle Anomaly and the theoretically cleanest extraction of $|V_{ud}|$ at the 0.02\% level, comparable to the deduction from superallowed beta decays., Comment: contribution to Snowmass 2021 based on the PIONEER proposal (arXiv:2203.01981)

A next-generation rare pion decay experiment, PIONEER, is strongly motivated by several inconsistencies between Standard Model (SM) predictions and data pointing towards the potential violation of lepton flavor universality. It will probe non-SM explanations of these anomalies through sensitivity to quantum effects of new particles even if their masses are at very high scales. Measurement of the charged-pion branching ratio to electrons vs. muons $R_{e/\mu}$ is extremely sensitive to new physics effects. At present, the SM prediction for $R_{e/\mu}$ is known to 1 part in $10^4$, which is 15 times more precise than the current experimental result. An experiment reaching the theoretical accuracy will test lepton flavor universality at an unprecedented level, probing mass scales up to the PeV range. Measurement of pion beta decay, $\pi^+\to \pi^0 e^+ \nu (\gamma)$, with 3 to 10-fold improvement in sensitivity, will determine $V_{ud}$ in a theoretically pristine manner and test CKM unitarity, which is very important in light of the recently emerged tensions. In addition, various exotic rare decays involving sterile neutrinos and axions will be searched for with unprecedented sensitivity. The experiment design benefits from experience with the recent PIENU and PEN experiments at TRIUMF and the Paul Scherrer Institut (PSI). Excellent energy and time resolutions, greatly increased calorimeter depth, high-speed detector and electronics response, large solid angle coverage, and complete event reconstruction are all critical aspects of the approach. The PIONEER experiment design includes a 3$\pi$ sr 25 radiation length calorimeter, a segmented low gain avalanche detector stopping target, a positron tracker, and other detectors. Using intense pion beams, and state-of-the-art instrumentation and computational resources, the experiments can be performed at the PSI ring cyclotron.

Let $A$ and $B$ be Banach algebras with bounded approximate identities and let $\Phi:A\to B$ be a surjective continuous linear map which preserves two-sided zero products (i.e., $\Phi(a)\Phi(b)=\Phi(b)\Phi(a)=0$ whenever $ab=ba=0$). We show that $\Phi$ is a weighted Jordan homomorphism provided that $A$ is zero product determined and weakly amenable. These conditions are in particular fulfilled when $A$ is the group algebra $L^1(G)$ with $G$ any locally compact group. We also study a more general type of continuous linear maps $\Phi:A\to B$ that satisfy $\Phi(a)\Phi(b)+\Phi(b)\Phi(a)=0$ whenever $ab=ba=0$. We show in particular that if $\Phi$ is surjective and $A$ is a $C^*$-algebra, then $\Phi$ is a weighted Jordan homomorphism.

$C^*$-algebras, group algebras, and the algebra $\mathcal{A}(X)$ of approximable operators on a Banach space $X$ having the bounded approximation property are known to be zero product determined. We are interested in giving a quantitative estimate of this property by finding, for each Banach algebra $A$ of the above classes, a constant $\alpha$ with the property that for every continuous bilinear functional $\varphi\colon A \times A\to\mathbb{C}$ there exists a continuous linear functional $\xi$ on $A$ such that \[ \sup_{\Vert a\Vert=\Vert b\Vert=1}\vert\varphi(a,b)-\xi(ab)\vert\le \alpha\sup_{\mathclap{\substack{\Vert a\Vert=\Vert b\Vert=1, \\ ab=0}}}\vert\varphi(a,b)\vert. \]

Polycrystalline bulk Mn:ZnO ceramics with Mn nominal concentrations of 6, 11, 17 and 22 at.% were prepared trough solid-state reaction method and subjected to a heat treatment in reducing atmosphere (Ar (95%) and H2 (5%)). The samples were studied with particular emphasis on their compositions, structural, and magnetic properties. A detailed microstructural and chemical analysis confirms the Mn doping of the wurtzite ZnO structure mainly at the surface of the ZnO grains. For the samples with higher Mn content, the secondary phases ZnMn2O4 and Mn1-xZnxO (Zn-doped MnO) were detected for the as prepared and the heat treated samples, respectively. The structural change of the secondary phases under heat treatment, from ZnMn2O4 to Mn1-xZnxO, confirms the effectiveness of the heat treatment in to reduce the valence of the metallic ions and in the formation of oxygen vacancies into the system. In spite of the induced defects, the magnetic analysis present only a paramagnetic behavior with an antiferromagnetic coupling between the Mn ions. In the context of the bound magnetic polaron theory, it is concluded that oxygen vacancies are not the necessary defect to promote the desired ferromagnetic order at room temperature., Comment: 19 pages; 7 figures

The nature of the often reported room temperature ferromagnetism in transition metal doped oxides is still a matter of huge debate. Herein we report on room temperature ferromagnetism in high quality Co-doped ZnO (Zn1-xCoxO) bulk samples synthesized via standard solid-state reaction route. Reference paramagnetic Co-doped ZnO samples with low level of structural defects are subjected to heat treatments in a reductive atmosphere in order to introduce defects in the samples in a controlled way. A detailed structural analysis is carried out in order to characterize the induced defects and their concentration. The magnetometry revealed the coexistence of a paramagnetic and a ferromagnetic phase at room temperature in straight correlation with the structural properties. The saturation magnetization is found to increase with the intensification of the heat treatment, and, therefore, with the increase of the density of induced defects. The magnetic behavior is fully explained in terms of the bound magnetic polaron model. Based on the experimental findings, supported by theoretical calculations, we attribute the origin of the observed defect-induced-ferromagnetism to the ferromagnetic coupling between the Co ions mediated by magnetic polarons due to zinc interstitial defects., Comment: 33 pages, 9 figures

Let $\mathcal{M}$ be a von Neumann algebra, and let $0

Using the approach based on the Bogoliubov inequality for free energy, we have studied the magnetic properties of the spin-3/2 Blume-Capel quantum model in the presence of the random transverse single-ion anisotropy (RTSIA). By analyzis of the phase diagrams in $\tau \times \varphi_{x} $, $m \times \varphi_{x}$ and $m \times \tau$ plans, we have obtained information about how the presence of anisotropy affects the properties of the system. We have shown that the RTSIA is responsible for changing the topology of the phase diagrams, compared to the pure model, leading to the appearance tricritical point (TCP)., Comment: 14 pages, 5 figures

In this work, we have performed Monte Carlo simulations to study phase transitions in a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on the square and cubic lattices and with two different single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins $S^A = 1$ (states $\pm1$ and 0) on the sublattice $A$ and $S^B = 3/2$ (states $\pm 3/2$, $\pm 1/2$) on the sublattice $B$. We have used single-ion anisotropies $D_{A}$ and $D_{B}$ acting on the sites of the sublattice $A$ and $B$, receptively. We have determined the phase diagrams of the model in the temperature $T$ versus the single-ion anisotropies strength $D_A$ and $D_B$ plane and shown that the system exhibits both second- and first-order phase transitions. We also have shown that this system displays compensation points for some values of the anisotropies.

Let $\mathcal{M}$ be a von Neumann algebra with a normal semifinite faithful trace $\tau$. We prove that every continuous $m$-homogeneous polynomial $P$ from $L^p(\mathcal{M},\tau)$, with $0

Let $G$ be a compact group, let $X$ be a Banach space, and let $P\colon L^1(G)\to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $\Phi\colon L^1(G)\to X$ such that $P(f)=\Phi \bigl(f\ast\stackrel{n}{\cdots}\ast f \bigr)$ for each $f\in L^1(G)$. We also seek analogues of this result about $L^1(G)$ for various other convolution algebras, including $L^p(G)$, for $1< p\le\infty$, and $C(G)$.

Let $X$ and $Y$ be Banach spaces, let $\mathcal{A}(X)$ stands for the algebra of approximable operators on $X$, and let $P\colon\mathcal{A}(X)\to Y$ be an orthogonally additive, continuous $n$-homogeneous polynomial. If $X^*$ has the bounded approximation property, then we show that there exists a unique continuous linear map $\Phi\colon\mathcal{A}(X)\to Y$ such that $P(T)=\Phi(T^n)$ for each $T\in\mathcal{A}(X)$., Comment: To appear in Linear and Multilinear Algebra

In this paper we present a study of the effects of two different single-ion anisotropies in the phase diagram and in the compensation temperature of the mixed spin-2 and spin-5/2 Ising ferrimagnetic system. We employed the mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. Also we found the Landau expansion of the free energy in the order parameter to describe the phase diagrams. In the plane critical temperature versus single-ion anisotropie the phase diagram displays tricritical behavior. The critical and compensation temperatures increase when the single-ion anisotropies increase., Comment: 8 pages, 5 figures

In this work we study a disordered binary Ising model on the square lattice. The model system consists of two different particles with spin-1/2 and spin-1, which are randomly distributed on the lattice. It has been considered only spin nearest-neighbor exchange interactions with $J>0$. This system can represent a disordered magnetic binary alloy $A_{x}B_{1-x}$, obtained from the high temperature quenching of a liquid mixture. The results were obtained by the use of Monte Carlo simulations for several lattice sizes $L$, temperature $T$ and concentration $x$ of ions $A$ with spin-1/2. We found its critical temperature, through the reduced fourth-order Binder cumulant for the several values of the concentration $x$ of particles (spin-1/2, spin-1), and also the magnetization, the susceptibility and the specific heat as a function of temperature $T$., Comment: 7 pages, 7 figures

We show within a local self-consistent mean-field treatment that a random distribution of magnetic adatoms can open a robust gap in the electronic spectrum of graphene. The electronic gap results from the interplay between the nature of the graphene sublattice structure and the exchange interaction between adatoms.The size of the gap depends on the strength of the exchange interaction between carriers and localized spins and can be controlled by both temperature and external magnetic field. Furthermore, we show that an external magnetic field creates an imbalance of spin-up and spin-down carriers at the Fermi level, making doped graphene suitable for spin injection and other spintronic applications., Comment: 5 pages, 5 figures