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Titlebook: Introduction to Conformal Invariance and Its Applications to Critical Phenomena; P. Christe,M. Henkel Book 1993 Springer-Verlag Berlin Hei

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发表于 2025-3-21 16:22:54 | 显示全部楼层 |阅读模式
书目名称Introduction to Conformal Invariance and Its Applications to Critical Phenomena
编辑P. Christe,M. Henkel
视频video
丛书名称Lecture Notes in Physics Monographs
图书封面Titlebook: Introduction to Conformal Invariance and Its Applications to Critical Phenomena;  P. Christe,M. Henkel Book 1993 Springer-Verlag Berlin Hei
描述The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau‘s general theory of critical phenomena. In a dramatic development, Onsager‘s exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in th
出版日期Book 1993
关键词Hamiltonian; Renormalization group; Superconductor; Universe; atmosphere; carbon; carbon dioxide; developme
版次1
doihttps://doi.org/10.1007/978-3-540-47575-0
isbn_softcover978-3-662-13922-6
isbn_ebook978-3-540-47575-0Series ISSN 0940-7677
issn_series 0940-7677
copyrightSpringer-Verlag Berlin Heidelberg 1993
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发表于 2025-3-21 23:28:13 | 显示全部楼层
Conformal Invariance and the Stress-Energy Tensor,s with short-ranged interactions, it is reasonable to suppose that global scale invariance . generalizes to local scale invariance .. However such transformations may change the global geometry of the system, therefore affecting the local covariant transformation properties of the scaling operators.
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Representation Theory of the Virasoro Algebra,ols needed are the representation theory of the Virasoro algebra and the operator product algebra and we now give a detailed presentation of the technical points required. The first application of this will be to the Ising model in chapter 6.
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The Ising Model Correlation Functions,ry operators, read from the Kac table (Table 5), reduces to the identity operator . = ø. (conformal weights . which contains the stress-energy tensor, the spin-density ., and the energy-density .. The central charge is . = 1/2 and the model is labeled by . = 3 in the Kac notation (eqs. (4.48) and (4
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The Hamiltonian Limit and Universality,idean time evolution operator, we were led to define a corresponding quantum Hamiltonian. While in general, this will have a rather complicated form, there is a limit procedure, called the ., to simplify the structure of the transfer matrix considerably without affecting the universal properties of
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Numerical Techniques,f diagonalizing . can be broken into the separate consideration of block-diagonal parts by using a few simple symmetry properties. In connection with conformal invariance, the systematic use of translation invariance allows to fix the normalization of . in a unique way. Numerical diagonalization and
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