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We connected the two ends of a finite spin-1/2 antiferromagnetic Ising chain with a magnetic impurity at one end to form a closed ring, and studied its magnetic susceptibility exactly by using the transfer matrix method. We calculated the magnetic susceptibility in the whole temperature range and gave the phase diagram at ground state of the system about the anisotropy of the impurity and strength of the connection exchange interaction for spin-1 and -3/2 impurities. We also gave the ground state entropy of the system and derived the asymptotic expression of the magnetic susceptibility multiplied by temperature at the zero-temperature limit and the high-temperature limit. It was found that a degenerate phase may exist in some parameter region at zero temperature for the odd spin number system, and the ground state entropy is ln(2) in the nondegenerate phase and is dependent on the spin number in the degenerate phase. The magnetic susceptibility of the system at low temperature exhibits ferromagnetic behavior, and the Curie constant is related to the spin configuration at ground state. When the ground state is nondegenerate, the Curie constant is equal to the square of the net spin, regardless of the parity of the number of the spin. When the spin number is odd and the ground state is degenerate, the Curie constant may be related to the total spin number. At the high-temperature limit, the magnetic susceptibility multiplied by temperature is related to the spin quantum number of the impurity and the spin number in the ring. Key words: transfer matrix method, magnetic susceptibility, magnetic impurity, Ising ring, Curie's law. Nous connectons les deux bouts d'une chaine d'Ising finie de spin 1/2 antiferromagnetique avec une impurete magnetique a un bout, dans le but d'etudier de facon exacte la susceptibilite magnetique en utilisant la methode de la matrice de transfert. Nous calculons la susceptibilite magnetique dans le domaine complet de temperature. Nous presentons aussi le diagramme de phase dans le fondamental du systeme touchant l'anisotropie de l'impurete et la force de l'interaction d'echange, pour les impuretes de spin 1 et 3/2. Nous donnons aussi l'entropie du fondamental du systeme et derivons l'expression asymptotique de la susceptibilite magnetique multipliee par la temperature a la limite de temperature zero et a la limite de haute temperature. Nous trouvons qu'une phase degeneree peut exister dans certaine region parametrique a temperature zero pour un nombre impair de spins du systeme oU l'entropie du fondamental du systeme est ln(2) dans la phase non degeneree, alors qu'elle est dependante du nombre de spin dans la phase degeneree. La susceptibilite magnetique du systeme a basse temperature a un comportement ferromagnetique et la constante de Curie est reliee a la configuration de spin dans l'etat fondamental. Quand le fondamental est non degenere, la constante de Curie est egale au carre du spin net, sans regard au caractere pair/impair du nombre de spins dans l'anneau. Lorsque le nombre de spins est impair et que le fondamental est degenere, la constante de Curie peut etre reliee au nombre total de spins. Dans la limite de haute temperature, la susceptibilite magnetique multipliee par la temperature est reliee au nombre quantique de spin de l'impurete et au nombre de spins dans l'anneau. [Traduit par la Redaction] Mots-cles : methode de la matrice de transfert, susceptibilite magnetique, impurete magnetique, anneau d'Ising, loi de Curie., 1. Introduction In condensed matter physics, the variants of low-dimensional quantum antiferromagnetic system have received much attention due to their low dimensionality and a novel phenomenon arising from the quantum [...]

As a pillar industry with high energy consumption and low efficiency, the building industry of China has produced consistently high carbon emission levels in recent years. The important goals in the coordinated development of this industry include the large-scale development of green buildings, the use of energy technologies to reduce carbon emissions, and an effective reduction of carbon intensity. Prefabricated buildings have become popular in this industry due to their low energy consumption, emission, and pollution and environment-friendly nature. This paper examines those factors that influence the carbon emissions from the construction of prefabricated buildings across three phases, namely, production in plants, logistics transportation, and assembly construction, builds an evaluation index system for studying the carbon emissions in the materialization phase of prefabricated buildings, and employs the hierarchical fuzzy comprehensive evaluation method to construct an evaluation model. Results show that the overall energy consumption of prefabricated buildings is lower than that of traditional concrete pouring-type buildings. The hierarchical fuzzy comprehensive evaluation model is scientific and reasonable when used to measure the comprehensive benefits of carbon emissions from prefabricated buildings. By taking a project in Zhengzhou City, Henan Province as an example, the comprehensive evaluation results show that the carbon emissions of this project are at moderate levels. The carbon emissions from prefabricated buildings can be reduced by expanding the market scale of the building industry, adjusting its use of building materials, and setting up special funds for these buildings. The findings of this work provide a certain reference value for analysing the differences between prefabricated and traditional buildings in terms of their carbon emissions in the materialization phase, for evaluating how the carbon emissions of the former can be reduced, and for formulating and executing building emission reduction plans.