We establish a correspondence between the free-field construction and the minimal-model construction of the Calabi–Yau sector of the four-dimensional heterotic string compactified on Berglund–Hübsch type Calabi–Yau manifolds and their orbifolds. For Fermat-type polynomials the Calabi–Yau vertex operators expressed in terms of free fields are shown to correspond to products of primary fields of ????=2 minimal models. Using this correspondence we verify modular invariance of the free-field construction and extend it to Berglund–Hübsch Calabi–Yau orbifolds, deriving the conditions on complete vertex operators that parallel those of the minimal-model construction [1]. [1] A. Belavin, D. Gepner, G. Makarov, Free-Field Construction of Heterotic String Compactified on Calabi–Yau Orbifolds via Correspondence with N=2 SCFT Minimal Models, Nucl. Phys. B 117668 (2026).

The Berry curvature effect in anomalous transport driven by statistical forces such as the gradient of temperature or chemical potential has been developed by Di Xiao et al in Phys. Rev. Lett. 97, 026603 (2006). This theory operates with spinless fermions. So, the Berry curvature, corresponding magnetic moment of wave packets and the magnetic field dependent density of states originate from the electron orbital degrees of freedom. We present an alternative derivation of the Berry curvature effect on charge, heat and as well on thermalelectric currents in altermagnets and noncentrosymmertric metals where the electron band dispersion possesses spin dependent band splitting.

The band spin splitting in the hexagonal altermagnet CrSb is established using the magnetic group formalism that allows to find the additional spin splitting missed in the frame of the exchange approximation.

Phys.Rev.B 114, 065130 (2026).

Altermagnets are substances with a momentum-dependent spin splitting of electron bands due to a specific crystal structure that is invariant under time reversal only in combination with rotations and reflections. The developed phenomenological approach allows to obtain a spectrum of electron bands in altermagnets corresponding to antiferromagnets with the same symmetry. We consider antiferromagnetic, weak ferromagnetic, and ferrimagnetic structures. The calculated Berry curvature of electron bands in the alterrmarnet with zero spontaneous magnetisation occurs an odd function of momentum whereas it is even in a weak ferromagnetic state. The Berry curvature in ferrimagnetic state is equal to zero.

In this work, we propose an algorithm for constructing orbifolds of Calabi-Yau manifolds of Berglund-Hubsch type. This approach allows us to obtain all mirror pairs for Calabi-Yau manifolds of this type. As an example, we considered one of the Fermat-type models, for which all its orbifolds and their mirror pairs were found, and also for each orbifold the number of generations of quarks and leptons was found, as well as the number of types of particles participating only in gravitational interaction, i.e. dark matter particles.

We discuss the electron dynamics on complex Fermi surfaces in the presence of rather strong magnetic fields. Such electron dynamics can be quite complex, and its most complex regimes are associated with the dynamics of analytic systems on Riemann surfaces. In general, this dynamics is associated with the most complex angular diagrams describing the behavior of conductivity in strong magnetic fields. The detection of such diagrams is of great interest, however, it requires a very careful selection of experimental parameters. Here we discuss the emergence of such diagrams for dispersion relations arising in tight-binding and nearly free electron models in the cubic lattice case.

We consider the Novikov problem, i.e. the problem of describing the global geometry of the level sets of quasiperiodic functions in the plane, for potentials formed by the superposition of periodic potentials that share the same rotational symmetry. For this class of potentials, it is shown that unbounded components of the level sets can exist at only a single energy level; in this respect, such potentials are similar to random potentials in the plane.

Various types of electrohydrodynamic instabilities in liquid crystals (LCs) are a recurring theme in LC research. However, the nonlinear stage of the flexoelectric instability in nematics remains the least studied aspect of this phenomenon. The report will highlight a key advancement in nonlinear physics, providing a compelling example of nonlinear dynamical system behavior. By solving the system of nonlinear equations for a nematic in an alternating external field, we derive from first principles the unique "dancing" behavior of truly two-dimensional patterns above the flexoelectric instability threshold. Our analysis is restricted to liquid crystals with negative dielectric permittivity and electrical conductivity anisotropies. The resulting solution represents a stable limit cycle near above the Hopf bifurcation, valid within the parameters range where the solutions characteristic exponent is complex. The generalized two-dimensional Ginzburg-Landau-like phenomenological theory of the phenomenon is developed. A comprehensive stability analysis of the one-dimensional and two-dimensional solutions of the nonlinear dynamical system for nematics driven by an external alternating electric field of amplitude above the flexoelectric instability threshold is carried out under a change of the control parameters.

1. "Dancing" Two-dimensional Patterns in Nematics above the Flexoelectric Instability Threshold, E.S. Pikina, JETP Letters (2026), DOI: 10.1134/S0021364026608900, Open Access на сайте Pleiades — Springer Nature по решению редколлегии журнала JETP Letters ["Танцующие" двумерные структуры выше порога флексоэлектрической неустойчивости", Е.С.Пикина, Письма в ЖЭТФ, т. 124 (9), 476 (2026), DOI: 10.7868/S3034576626110087].
2. "Pattern formation in nonlinear dynamics of nematic liquid crystals above the flexoelectric instability threshold," E.S. Pikina, A.R. Muratov, E.I. Kats, V.V. Lebedev, Physics of Fluids, vol. 38, Issue 8, 087101 (2026), https://doi.org/10.1063/5.0343775 .

Rare-earth tritellurides (RTe3) exhibit a wide range of electronic properties, spanning from the emergence of charge-density waves (CDWs) to superconductivity. Angle-resolved photoemission spectroscopy (ARPES) serves as an effective technique for investigating changes in band structure and symmetry associated with CDW formation. Despite several advantages, obtaining an accurate two-dimensional map of the bands in momentum space via ARPES presents certain challenges, often stemming from limited energy or momentum resolution, among other factors. Consequently, the study of magnetoresistance and magnetic quantum oscillations (MQOs) in rare-earth tritellurides provides complementary insights into their electronic structure and phase diagram. In the first study [1], we apply image-processing techniques to ARPES data to determine the dimensions of residual electronic pockets in RTe3 compounds. The results are compared with measurements of slow quantum oscillations, which helps clarify the nature of these oscillations at temperatures below the phase transitions associated with CDW1 and CDW2. The strong agreement between the results obtained via these two methods sheds light on the nature of the persistent metallic states and demonstrates the efficacy of using image-segmentation techniques to refine the analysis of electronic structure based on ARPES data. However, for certain frequencies, a good agreement between the ARPES and MQO data is not achieved. By analyzing the experimental MQO data across various RTe3 compounds—examining both resistance and magnetization—we conclude that some of these oscillations are "difference" (slow) oscillations, the frequencies of which correspond to the difference in the areas of the Fermi surface pockets. Beyond MQOs, the behavior of the non-oscillatory (monotonic) component of the magnetoresistance is also of significant interest. In particular, anisotropic jumps in magnetoresistance are observed during antiferromagnetic transitions in GdTe3 [2]; these features help refine the magnetic phase diagram of such compounds and offer a method for investigating magnetic ordering via transport measurements—an approach applicable to many other compounds. A theoretical interpretation of these magnetoresistance jumps is provided [2]. It should be noted that determining antiferromagnetic (AFM) ordering in GdTe3 via neutron scattering is challenging, as Gd atoms are strong neutron absorbers. 1. A.A. Morocho, P.D. Grigoriev, Jian-Qiao Meng, Reconciliation of ARPES and magnetic quantum oscillation data via image processing in rare-earth tritellurides, Eur. Phys. J. Plus 141, 62 (2026). 2. A.A. Sinchenko, P.D. Grigoriev, A.Hadj-Azzem, E.Pachoud, E. Lorenzo and P. Monceau, Contribution to the GdTe_3 magnetic phase diagram from electronic transport measurements, sent to Phys. Rev. B.

The giant temperature hysteresis of electrical resistance recently discovered in EuTe4 is a record-breaking phenomenon among crystalline solids, yet its underlying mechanism remains a mystery. In this work, we propose an interpretation of this hysteresis in EuTe4 as the result of an interplay between two electronic instabilities: band anti-crossing (repulsion) at the Fermi level and a charge-density wave. By calculating the electronic susceptibility and its temperature dependence at the wave vector of the charge-density wave, both with and without accounting for band anti-crossing, we have arrived at an estimate for the width of the temperature hysteresis observed in electrical resistance measurements of EuTe4. These calculations require accounting for the contributions of various combinations of bands that cross the Fermi level, which originate from the mono- and bilayer p-orbitals of tellurium.

Based on an analysis of results obtained using the numerical Monte Carlo method for a system of hard spheres, it has been established that the quantum contribution to its energy is proportional to the first power of Planck's constant. An interpolation formula for heat capacity is derived and justified. For a system of hard spheres, this formula exhibits a "fan point" (bifurcation-like point) that separates high-temperature and low-temperature regimes. The study concludes with a comparison between this model system and physical liquid He4, for which such a fan point is observed experimentally. Near this point, both the model system and liquid He4 exhibit an identical linear dependence of pressure on temperature, a characteristic typical of an ideal, as well as an identical dependence of entropy on dimensionless density.