Direct Calculation of Thermodynamic Quantities for Heisenberg Model

The XXX Heisenberg model is studied at finite temperature. The free energy is derived without recourse to Thermal Bethe Ansatz method and Quantum Transfer Matrix method. The result perfectly agrees with the free energy derived by Thermal Bethe Ansatz method. An explicit expression of the cluster expansion coefficient in arbitrary order is presented for the first time.Comment: 26 page

Deciphering the Drivers of Smart Livestock Technology Adoption in Japan: A Scoping Review, Expert Interviews, and Grounded Theory Approach

With global demand for animal products projected to increase significantly by 2050, understanding the factors that influence the adoption of smart livestock technologies has become increasingly crucial. Conducted within the unique agricultural context of Japan, our study builds upon traditional theoretical frameworks that often oversimplify farmers' decision-making processes. By employing a scoping review, expert interviews, and a Modified Grounded Theory Approach, our research uncovers the intricate interplay between individual farmer values, farm management policies, social relations, agricultural policies, and livestock industry trends. We particularly highlight the unique dynamics within family-owned businesses, noting the tension between an "advanced management mindset" and "conservatism." Our study underscores technology adoption's sequential and iterative nature, intricately tied to technology availability, farmers' digital literacy, technology implementation support, and observable technology impacts on animal health and productivity. Despite certain limitations, our findings carry profound implications for stakeholders, providing valuable insights to overcome adoption barriers and advocating for more sustainable, efficient, and animal welfare-oriented livestock production systems. This research establishes a solid foundation for future explorations into smart livestock technology adoption.Comment: 56 pages, 3 figure

Mass and generalized Thiele equation of the magnetic skyrmion

An analytical expression is obtained to the mass of an isolated magnetic skyrmion and its linearized equation of motion. The magnetic skyrmion is viewed as a topologically protected spin-wave soliton in the magnetic ultrathin films stabilized by the interfacial-Dzyaloshinskii-Moriya interaction. The equations of motion are derived from the Landau-Lifshitz-Gilbert equation for both the skyrmion charge and magnetization centers. They are generalized Thiele equations, including gyro-term, dissipation term, external force, an acceleration term with the tensorial mass, and time derivatives of the external forces. The equation of motion of the center of the skyrmion charge essentially shows the massless nature of the skyrmion. In contrast, the equation of motion for the magnetization center results in a finite mass that is in the same order as the Doring mass density for the linear domain wall. Furthermore, the time derivative of the external force predominantly contributes to the immediate response of the skyrmion motion, i.e., the mass-less property remains even after the skyrmion acquires its kinetic mass. A micromagnetic simulation based on the LLG equation was performed for various magnetic parameters. Obtained trajectories at 0 K are compared with the theoretical predictions.Comment: 28 pages, 3 figure

Robust Model Selection for Classification of Microarrays

Recently, microarray-based cancer diagnosis systems have been increasingly investigated. However, cost reduction and reliability assurance of such diagnosis systems are still remaing problems in real clinical scenes. To reduce the cost, we need a supervised classifier involving the smallest number of genes, as long as the classifier is sufficiently reliable. To achieve a reliable classifier, we should assess candidate classifiers and select the best one. In the selection process of the best classifier, however, the assessment criterion must involve large variance because of limited number of samples and non-negligible observation noise. Therefore, even if a classifier with a very small number of genes exhibited the smallest leave-one-out cross-validation (LOO) error rate, it would not necessarily be reliable because classifiers based on a small number of genes tend to show large variance. We propose a robust model selection criterion, the min-max criterion, based on a resampling bootstrap simulation to assess the variance of estimation of classification error rates. We applied our assessment framework to four published real gene expression datasets and one synthetic dataset. We found that a state-of-the-art procedure, weighted voting classifiers with LOO criterion, had a non-negligible risk of selecting extremely poor classifiers and, on the other hand, that the new min-max criterion could eliminate that risk. These finding suggests that our criterion presents a safer procedure to design a practical cancer diagnosis system

Manipulating 1-dimensinal skyrmion motion by external magnetic field gradient

We have investigated an analytic formula of the 1-dimensional magnetic skyrmion dynamics under external magnetic field gradient. We find excellent agreement between the analytical model and micromagnetic simulation results for various magnetic parameters such as the magnetic field gradient, Gilbert damping constant. We also observe much faster velocity of the chiral domain wall (DW) motion. The chiral DW is exist with smaller interfacial Dzyaloshinskii-Moriya interaction energy density cases. These results provide to develop efficient control of skyrmion for spintronic devices.Comment: 15 pages, 5 figures, 1 tabl

A direct calculation of the free energy from the Bethe ansatz equation for the Heisenberg model

Thermodynamics of the XXX Heisenberg model is studied. The trace of the Boltzmann weight with respect to the Hilbert space is taken in the thermodynamic limit with the number of up-spins being fixed. The expression of the trace gives an explanation why the correct thermodynamic quantities are derived from the string hypothesis. Combining this with the previous result, we conclude that the free energy can be calculated only by assuming the Bethe ansatz equation. The method is more direct than other known methods which were used to derive the free energy.Comment: 52 pages, submitted to J. Math. Phy