We study the coupled twin-diamond chain, a decorated one-dimensional Ising model motivated by the magnetic structure of Cu_2(TeO_3)_2Br_2. By applying an exact mapping to an effective Ising chain, we obtain the full thermodynamic description of the system through a compact transfer-matrix formulation. The ground-state analysis reveals five distinct phases, including two frustrated sectors with extensive degeneracy. These frustrated regions give rise to characteristic entropy plateaus and separate the ordered phases in the zero-temperature diagram. At low temperatures the model exhibits peculiar sharp yet continuous variations of entropy, magnetization, and response functions, reflecting clear signatures of pseudotransition behavior. The coupled twin-diamond chain thus provides an exactly solvable setting in which competing local configurations and internal frustration lead to pronounced dual pseudocritical features in one dimension.

While true phase transitions are forbidden in one-dimensional systems with short-range interactions, several models have recently been shown to exhibit sharp yet analytic thermodynamic anomalies that mimic thermal phase transitions. We show that this behavior arises from transfer matrices that are mathematically irreducible but possess a nearly block-diagonal structure due to the weak contribution of off-diagonal Boltzmann weights in the low-temperature regime. This results in weakly coupled competing sectors whose eigenvalue competition produces abrupt crossovers without nonanalyticity, a mechanism we term nearly block-diagonal irreducible. A key thermodynamic signature of such pseudotransitions is that the residual entropy at the interface remains bounded between the residual entropies of the competing sectors. We develop a general spectral framework to describe this behavior and apply it to two representative models: the Ising chain with internal degeneracy (Doniach model) and a hexagonal nanowire chain with mixed spin-1/2 and spin-1 components. In the first case, we derive exact expressions for the pseudo-critical temperature and residual entropy. In the second, we reduce the full 1458×1458 transfer matrix via symmetry decomposition and construct a low-rank effective matrix that accurately captures the crossover between quasi-ferromagnetic and quasi-core-ferromagnetic regimes. Our results demonstrate that pseudotransitions can be understood as spectral phenomena emerging from irreducible but functionally decoupled structures within the transfer matrix.

We present a theoretical investigation of the magnetic and thermodynamic properties of the triangular spin-1/2 cluster with Dzyaloshinskii–Moriya (DM) interaction, described by a spin-1/2 Heisenberg Hamiltonian with antisymmetric exchange interactions. The energy spectrum and ground-state phase diagram reveal the presence of ferromagnetic (FM), ferrimagnetic (FI), and frustrated (FR) phases, strongly influenced by the total spin and the DM interaction. We analyze magnetization and susceptibility, showing that at low temperatures the system exhibits a characteristic 1/3 magnetization plateau, while thermal fluctuations suppress magnetic order at higher temperatures. The entropy and specific heat display residual entropies due to ground-state degeneracies, Schottky-type anomalies at intermediate temperatures, and additional low-temperature features related to phase transitions. Particular attention is given to the magnetocaloric effect (MCE), characterized by both direct and inverse regimes depending on the magnetic field variation. We find that the DM interaction enhances the complexity of the MCE, leading to nontrivial entropy variations as a function of the magnetic field. These results provide insights into the role of frustration and anisotropy in tuning the MCE of properties triangular spin clusters, with relevance to Cu3-based molecular magnets.

We present an exact analysis of a spin–pseudospin X sawtooth chain that incorporates three distinct valence states of copper ions and serves as a minimal model for one-dimensional cuprates composed of corner-sharing copper triangles. The model includes magnetic exchange and electrostatic coupling constants both along the base sites and between base and apex sites capturing the competition between spin and charge degrees of freedom. Using the transfer-matrix method, we derive exact expressions for the free energy and obtain an analytical condition defining the pseudo-critical line associated with pronounced thermodynamic anomalies. The ground-state analysis reveals, besides an antiferromagnetic phase, three frustrated phases characterized by distinct residual entropies. At finite temperatures, these zero-temperature phase boundaries evolve into narrow entropy ridges signaling pseudo-transitions between the corresponding quasi-phases. The specific heat and the avoided-crossing scale exhibit sharp but continuous peaks at the pseudo-critical temperature, whereas the physical correlation length may be controlled by a different subleading eigenvalue. Local correlation functions uncover a cooperative rearrangement from charge-dominated to magnetically correlated regimes. Our results demonstrate that the sawtooth geometry promotes frustration and short-range coherence leading to pronounced pseudo-transition behavior.

Conventional finite-size theories describe first-order coexistence through free-energy competition and interfacial tunneling, but the distinct spectral roles of sector balance and inter-sector connectivity are not usually explicit. We show that pseudo-transitions and thermodynamic phase coexistence are governed by two spectral coordinates: sector imbalance locates balance, while connectivity determines whether that balance remains avoided. At balance, finite connectivity produces a unique dominant state with equal spectral weights in the symmetrized two-sector representation. For short-range systems with positive interface tension, interfacial costs suppress the connectivity exponentially, close the coexistence splitting, and asymptotically restore reducibility. Thus, genuine phase coexistence emerges as the singular limit of finite-size avoided coexistence, whereas one-dimensional pseudo-transitions retain finite connectivity. In a decorated bilayer Ising model, the coexistence gap at independently est

We investigate the thermodynamic and quantum properties of a magnetoelastic spin-1/2 Heisenberg dimer, where the exchange interaction depends on the dimer displacement. By combining an exact treatment of the spin sector with a harmonic description of the vibrational degree of freedom, we obtain an effective model in which each spin configuration is associated with a distinct vibrational mode, leading to a non-factorizable partition function. We analyze the thermal behavior and identify regimes corresponding to entangled and fully polarized states. Quantum correlations are analyzed through concurrence and local quantum uncertainty, showing that while entanglement is rapidly suppressed by temperature, nonclassical correlations persist over a broader range due to the competition between spin sectors. We further examine the magnetic Fisher information, which provides a measure of the sensitivity of the system to the external magnetic field. Its behavior reveals enhanced response in crossover regions where magnetoelastic effects induce strong redistribution of the level populations. Our results demonstrate that magnetoelastic coupling plays a central role in controlling both quantum correlations and magnetic response, establishing a direct link between entanglement, nonclassical correlations, and thermodynamic sensitivity in coupled spin-dimer systems.

We investigate a quantum thermal machine composed of two qubits coupled through a Raman-induced exchange interaction and driven by inhomogeneous transition frequencies. The system is analyzed within Carnot, Otto, and Stirling thermodynamic cycles, including the Stirling cycle with and without regeneration. We identify the conditions under which the device operates as a heat engine, refrigerator, thermal accelerator, or heater. Efficiency maps and operational-mode diagrams reveal well-defined boundaries in parameter space, governed by the frequency ratio r=/ω, the coupling strength g, and the thermal gradient between reservoirs. The Carnot cycle exhibits sharp transitions between engine and refrigerator regimes, while the Otto cycle displays a richer structure with the coexistence of all operational modes. The Stirling cycle shows enhanced versatility and performance, particularly when assisted by a regenerator, where near-ideal efficiencies are achieved. Overall, the Raman-type interaction introduces a controllable left-right asymmetry that enables nontrivial manipulation of thermodynamic behavior through frequency tuning.

This research explores the effects of decoherence on local quantum Fisher information and quantum coherence dynamics in a spin-1/2 Ising-XYZ chain model with independent reservoirs at zero temperature. Contrasting these effects with those in the spin-1/2 Heisenberg XYZ model reveals intricate interactions among quantum coherence, entanglement, and environmental decoherence in spin systems. Analysis of coherence dynamics highlights differences between the original and hybrid models, showcasing increased entanglement due to Ising interactions alongside reduced coherence from environmental redistribution. L Q F I $LQFI$ proves more resilient than coherence in specific scenarios, emphasizing decoherence's varying impacts on quantum correlations. This research underscores the complexity of quantum coherence dynamics and the crucial role of environmental factors in shaping quantum correlations, providing insights into entanglement and coherence behavior under environmental influences and guiding future studies in quantum information processing and correlation dynamics.

We investigate a one-dimensional water-like lattice model with Van der Waals and hydrogen-bond interactions, allowing for particle number fluctuations through a chemical potential. The model, defined on a chain with periodic boundary conditions, exhibits three ground-state phases: gas, bonded liquid, and dense liquid, separated by sharp phase boundaries in the chemical potential and temperature plane. Using the transfer matrix method, we derive exact analytical results within the grand-canonical ensemble and examine the finite-temperature behavior. The system exhibits clear pseudotransition features, including sharp but analytic changes in entropy, density, and internal energy, along with finite peaks in specific heat and correlation length. To assess the role of thermodynamic constraints, we consider the behavior under fixed density through a Legendre transformation. This constrained analysis reveals smoother anomalies, such as entropy kinks and finite jumps in specific heat, contrasting with the sharper grand-canonical signatures. These results underscore the ensemble dependence of pseudotransitions and show how statistical constraints modulate critical-like behavior. We also verify that the residual entropy continuity criterion holds in the grand-canonical ensemble but is violated when the system is constrained. Our findings illustrate how even a simple one-dimensional model can mimic water-like thermodynamic anomalies.

The one-dimensional extended Hubbard model (EHM) in the atomic limit has recently been found to exhibit a curious thermal pseudo-transition behavior, which closely resembles first and second-order thermal phase transitions. This phenomenon, occurring at half-filling, is influenced by the quantum phase transition between the alternating pair (AP) and paramagnetic (PM) phases at zero temperature. In this study, we leverage this anomalous behavior to investigate the performance of quantum many-body machines, using the EHM as the working substance. Our analysis reveals that the quantum Otto engine, when operating in the anomalous region, closely mimics the ideal Carnot engine. In this region, both the work output and thermal efficiency of the Otto engine increase, approaching the performance of a Carnot engine. This highlights the potential of many-body systems, such as the EHM, in enhancing quantum thermodynamic performance. Our findings demonstrate that, although the second law of thermodynamics prevents engines from surpassing Carnot efficiency, the Otto engine can operate remarkably close to this limit in the anomalous region, offering insights into new directions for future research on quantum thermodynamic cycles and working substances.

We investigate the phase diagram of a quantum mixed-spin (1/2, 1/2, 1, 1) Heisenberg tetramer chain featuring bond-alternating antiferromagnetic nearest-neighbor exchange interactions and single-ion anisotropy. This model exhibits a rich phase structure comprising three gapped phases: the antiferromagnetic, topological valence-bond-solid (TVBS), and the trivial nonmagnetic phases (TnM). We identify a multicritical Wess-Zumino-Witten SU (2)1 point where two Ising critical lines merge, forming a higher-symmetry point that realizes conformal embedding on the lattice. Beyond this multicritical point, a Gaussian critical line emerges, determining the boundary between the TVBS and the TnM phases. Utilizing the tangential finite-size scaling method, we demonstrate the precision with which critical points and correlation length critical exponents can be extracted along this Gaussian line. Our results reveal rich critical phenomena induced by the interplay of bond-alternating exchange and anisotropic single-ion interactions in quantum many-body systems.

A theoretical study of an antiferromagnetically coupled spin system, specifically Cu 3 − X ( X=As, Sb ) $\text{Cu}_{3}-\text{X}(\text{X=As, Sb})$ , characterized by a slightly distorted equilateral triangle configuration is presented. Using the Heisenberg model with exchange and Dzyaloshinskii–Moriya interactions, g-factors, and an external magnetic field, three quantum machines are investigated using this system as the working substance, assuming reversible processes. For Cu 3 − X $\text{Cu}_{3}-\text{X}$ the magnetocaloric effect (MCE) is significant at low temperatures ( ≈ $\approx$ 1K) under a perpendicular magnetic field ( ≈ 5 T $\approx 5{\rm T}$ ). Although only the Cu 3 − As $\text{Cu}_{3}-\text{As}$ compound is considered, since the Cu 3 − Sb $\text{Cu}_{3}-\text{Sb}$ compound behaves quite similarly. How MCE influences the Carnot machine, which operates as a heat engine or refrigerator when varying the external magnetic field is analyzed. In contrast, the Otto and Stirling machines can operate as heat engines, refrigerators, heaters, or thermal accelerators, depending on the magnetic field intensity. The results indicate that enhanced MCE broadens the operating regions for these machines, with the Otto and Stirling machines primarily functioning as refrigerators and accelerators. The corresponding thermal efficiencies are also discussed for all operating modes.

In this paper, we investigate the thermal quantum correlations in a semiconductor double quantum dot system. The device comprises a single electron in a double quantum dot subjected to a longitudinal magnetic field and a transverse magnetic field gradient. The thermal entanglement of the single electron is driven by the charge and spin qubits. Utilizing the density matrix formalism, we derive analytical expressions for thermal concurrence and correlated coherence. The main goal of this work is to provide a good understanding of the effects of temperature and various parameters on quantum coherence. Additionally, our findings indicate that the transverse magnetic field can be employed to adjust the thermal entanglement and quantum coherence of the system. We also highlight the roles of thermal entanglement and correlated coherence in generating quantum correlations, noting that thermal correlated coherence is consistently more robust than thermal entanglement. This suggests that quantum algorithms based solely on correlated coherence might be more resilient than those relying on entanglement.

In this work, the synthesis, structural characterization, and magnetic properties of a series of dinuclear and trinuclear antiferromagnetic copper (II) complexes with different bridging ligands are studied. The research employs antiferromagnetic theoretical models and experimental data to analyze the magnetic characteristics, including magnetization plateaus, magnetic susceptibility, and entanglement entropy. The results demonstrate significant changes in the magnetization behavior of the complexes, revealing distinct 1/3 magnetization plateaus and saturation points corresponding to different exchange interactions. The entanglement entropy analyses further correlate these magnetic transitions, offering insights into the quantum behavior of these metal-containing spin-1/2 compounds at low temperatures. These results highlight the importance of ligand design in tuning the magnetic properties of copper (II) complexes, providing a foundation for future studies of similar antiferromagnetic systems.

This research explores the effects of decoherence on local quantum Fisher information and quantum coherence dynamics in a spin-1/2 Ising-XYZ chain model with independent reservoirs at zero temperature. Contrasting these effects with those in the spin-1/2 Heisenberg XYZ model reveals intricate interactions among quantum coherence, entanglement, and environmental decoherence in spin systems. Analysis of coherence dynamics highlights differences between the original and hybrid models, showcasing increased entanglement due to Ising interactions alongside reduced coherence from environmental redistribution. The local quantum Fisher information proves more resilient than coherence in specific scenarios, emphasizing decoherence is varying impacts on quantum correlations. This research underscores the complexity of quantum coherence dynamics and the crucial role of environmental factors in shaping quantum correlations, providing insights into entanglement and coherence behavior under environmental influences and guiding future studies in quantum information processing and correlation dynamics.

A theoretical study of an antiferromagnetically coupled spin system, specifically Cu3-X(X=As, Sb), characterized by a slightly distorted equilateral triangle configuration is presented. Using the Heisenberg model with exchange and Dzyaloshinskii-Moriya interactions, g-factors, and an external magnetic field, three quantum machines are investigated using this system as the working substance, assuming reversible processes. For Cu3-X the magnetocaloric effect (MCE) is significant at low temperatures (approximate to 1K) under a perpendicular magnetic field (approximate to 5T). Although only the Cu3-As compound is considered, since the Cu3-Sb compound behaves quite similarly. How MCE influences the Carnot machine, which operates as a heat engine or refrigerator when varying the external magnetic field is analyzed. In contrast, the Otto and Stirling machines can operate as heat engines, refrigerators, heaters, or thermal accelerators, depending on the magnetic field intensity. The results indicate that enhanced MCE broadens the operating regions for these machines, with the Otto and Stirling machines primarily functioning as refrigerators and accelerators. The corresponding thermal efficiencies are also discussed for all operating modes.

This article introduces the space of A-linearly correlated fuzzy complex numbers. Using this space, we study the stationary Schrödinger equation with boundary conditions are given by fuzzy complex numbers. This equation plays an special role in Quantum Mechanics describing the state of the system. We apply the formalism to the step potential, generating quantum results consistent with traditional quantum results.

Recently, a kind of finite-temperature pseudo-transition was observed in several quasi-one-dimensional models. In this work, we consider a genuine one-dimensional extended Hubbard model in the atomic limit, influenced by an external magnetic field and with the arbitrary number of particles controlled by the chemical potential. The one-dimensional extended Hubbard model in the atomic limit was initially studied in the seventies and has been investigated over the past decades, but it still surprises us today with its fascinating properties. We rigorously analyze its low-temperature behavior using the transfer matrix technique and provide accurate numerical results. Our analysis confirms that there is an anomalous behavior in the half-filled band, specifically occurring between the alternating pair (AP) and paramagnetic (PM) phases at zero temperature. Previous investigations did not deeply identify this anomalous behavior, maybe due to the numerical simplicity of the model, but from analytical point of view this is not so easy to manipulate algebraically because one needs to solve an algebraic cubic equation. In this study, we explore this behavior and clearly distinguish the pseudo-transition, which could easily be mistaken with a real phase transition. This anomalous behavior mimics features of both first- and second-order phase transitions. However, due to its nature, we cannot expect a finite-temperature phase transition in this model.

Modeling in physics is often faced with challenges in terms of measurement uncertainty. Oscillations are observed in many real-world systems, in particular, in electrical circuits. One of the ways to insert the uncertainty present in some elements of an electrical circuit is to use fuzzy sets. To get insight into this issue, in this work, a mathematical model describing an linear oscillator is considered by assuming its initials conditions has uncertainty in terms of fuzzy numbers linearly correlated. The system obtained is known as fuzzy initial value problem (FIVP). Solutions of the FIVP are obted using fuzzy Laplace transform for linearly correlated process. We propose to analyze the dynamics of an RLC-type electrical circuit with initial conditions given by linearly correlated fuzzy numbers. According to the oscillations described by the circuit three types of damped oscillators are considered comprising underdamped, critically damped, and overdamped. For the underdamped case, the formalism presented here allows a first approximation analysis of an RLC circuit in the transient phase and subjected to impulsive transients (pulse).