Condensed Matter

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.

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.

We study the local electrostatic response of a charged superfluid in the presence of a cylindrically symmetric vortex, allowing both the particle density and the thermodynamic compressibility to vary with the radial coordinate. Starting from the electrostatic charge response obtained from the phase-only Popov action, we introduce a local-density extension and derive the regular near-axis expansion of the scalar potential. The constant, quadratic, and quartic coefficients are obtained explicitly in terms of the local screening response and of the leading nonuniform contribution to the vortex density profile. For a three-dimensional unitary Fermi equation of state, the density dependence of the compressibility generates a definite thermodynamic contribution to the quartic coefficient. The resulting decomposition separates this equation-of-state contribution from the ordinary constant-screening and charge-source terms that occur at the same order. This provides a compact analytical connection between vortex-core thermodynamics and the local electrostatic profile of a charged superfluid.