The theoretical description of phase transitions in condensed matter represents one of the most profound and enduring challenges in modern physics, spanning more than a century of intellectual development. From the phenomenological models of van der Waals in 1873 and Landau in 1937, through the statistical-mechanical rigor of integral equation theories of Ornstein and Zernike in 1914, Percus and Yevick in 1958, to Wilson’s renormalization group in 1971 and contemporary spectral methods such as the Self-Consistent Spectral Potential Mean-Field (SC-SPMF) method of Villani, the theoretical landscape has evolved through successive refinements that have progressively deepened our understanding of critical phenomena, metastability, and universality. Despite these remarkable advances, the prediction of phase transition temperatures, the characterization of critical behavior, and the understanding of metastability and hysteresis remain active areas of research, particularly for first-order transitions such as melting and crystallization. This review develops a central thesis: the difficulty of describing phase transitions in condensed matter arises from the intrinsically irreducible complexity of N-body systems. The behavior of a system of N interacting particles cannot, in general, be reduced to the behavior of N independent two-body systems. This is the essence of the N-body problem: the interactions between particles create collective effects that cannot be understood by considering pairwise interactions in isolation. The irreducible nature of this problem manifests itself in the hierarchy of correlation functions, where the n-body distribution function depends on the (n + 1)-body distribution function, leading to an infinite hierarchy that cannot be closed without approximations. The SC-SPMF method resolves the complexity of the problem through a spectral reduction that transforms the irreducible N-body problem into a self-consistent two-body problem in a mean field. The spectral criterion for phase transitions introduced by the SC-SPMF method represents a fundamental departure from traditional approaches: the transition is marked by a change in the curvature of the first eigenvalue μ1 (T). This criterion does not rely on arbitrary thresholds but on a qualitative change in the spectral response of the system, reflecting a fundamental change in the nature of correlations. The review is organized into three main parts. The first establishes the historical and conceptual foundations, tracing the evolution of theoretical approaches from van der Waals to the renormalization group, examining the successes and limitations of each approach, and identifying the common thread of approximate closures and functionals that has motivated the development of alternative methods. The second addresses the fundamental problem of complexity in N-body systems, exploring the BBGKY hierarchy, the irreducibility of many-body correlations, and the failure of pairwise reduction; it then presents the spectral mean-field approach as a rigorous solution to this problem, demonstrating how the eigenvalue spectrum of the Fisher operator encodes the collective behavior of the system. The third provides a comprehensive account of the SC-SPMF method. The SC-SPMF method offers several distinct advantages over existing approaches: it requires no approximate closures (unlike integral equation theories), no excess free energy functionals (unlike density functional theory), and no extensive computational resources (unlike molecular dynamics or Monte Carlo simulations). The coordination shell structure emerges self-consistently from the spectral decomposition, and the method naturally captures hysteresis and metastability because the self-consistent cycle provides stable solutions as long as the Fisher equation yields negative eigenvalues. The predictive power of the method is demonstrated by its ability to reproduce experimental structural parameters and to reveal the path-dependent universality that has not been observed in previous theoretical studies.
There are two models that explain the incommensurate elastic neutron scattering from La2−xBaxCuO4 (x=18), (i) spin spiral and (ii) collinear spin stripe. I show that available μSR data taken with a polycrystalline sample is consistent with the generic (arbitrary parameters) coplanar spin spiral. On the other hand for consistency with the collinear spin stripe one needs fine tuning of the parameters of the model. I also propose a further μSR experiment with a single crystal aimed specifically at the window of parameters where the spin stripe model is still consistent with the data. In the proposed experiment, the expected signals for these two models are dramatically different. Such an experiment would finally reject one of the models.
Imaging with cosmic-ray muon-induced secondary radiation complements muon transmission radiography and muon scattering tomography by exploiting the electrons and bremsstrahlung photons created along the muon track inside the target. Because these secondaries are produced predominantly at low energies, the performance of such a system depends critically on parameters that are usually treated as routine: the uniformity of the response of the surrounding scintillator array and the energy threshold applied during acquisition. This contribution reports the instrumental characterization of the muon camera (MUCA) setup operated at the University of Novi Sad, comprising a five-layer Close Cathode Chamber tracker and four large-area plastic scintillation detectors. Over a continuous run of about 24 h, the combined tracking efficiency was about 0.96 and stable at the percent level. Single-detector and joint spectra recorded with 137Cs and a bulk KCl source were used to equalize the high voltage across the array, and the acquisition threshold was set to approximately 230 keV. A direct comparison of images of a copper cylinder reconstructed with a 250 keV and with a 1 MeV analysis cut shows that the conventional MeV-level threshold discards the majority of the target-related signal. The corresponding limitation of the geometrical acceptance is also discussed. The design of the COMIS upgrade, which extends the scintillator coverage to the forward region and introduces a compact multi-channel readout, is outlined together with a first map of the light collection uniformity of its large-area scintillators.
Cadmium zinc telluride (CZT) detectors offer versatility, operational simplicity, and room-temperature X- and gamma-ray spectroscopy, making them attractive for collider applications, yet their use under high-flux conditions remains limited. Here, we present a preliminary feature-based pulse-shape analysis employing machine learning, on data acquired with a quasi-hemispherical CZT detector at the DANE beam test facility of the National Laboratory of Frascati of INFN. A 300-MeV electron beam impinging on a lead target produced characteristic Pb X-rays together with a broad background extending up to the electron-positron annihilation region. Physically motivated temporal and morphological features were extracted from the recorded waveforms and used to distinguish nominal photon-like pulses from anomalous events. An XGBoost classifier trained and validated on 10,000 labeled waveforms achieved an accuracy of approximately 97
Gold nanoparticles are of interest in a broad class of research fields, ranging from the basic sciences through technology to the biosciences. Not only are the environments in which they are investigated very diverse, but the temperature range is also very wide, going from cryogenic temperatures to hundreds of degrees Celsius. A primary role in all the potential applications is played by the electronic properties of the nanoparticles. While these have been studied theoretically before, less attention has been given to the potential effect of temperature on them. Here, we use a particle model and model Hamiltonian to study these possible effects by means of the finite-temperature Green function formalism. We focus in particular on how much temperature would impact observations in positron annihilation and in Compton scattering experiments. For our study, we consider temperatures ranging from −80 °C to 1000 °C and nanoparticle diameters ranging from 1 nm to 6 nm. We find that the temperature effects are rather small and generally at the limit of experimental resolution. Still, changes near the Fermi momentum in the Compton profiles should be observable in some cases.
