精确可解模型：严格处理有限核系统中相变的途径
Exactly Solvable Models: The Road towards a Rigorous Treatment of Phase Transitions in Finite Nuclear Systems
摘要：
我们讨论了最近获得的一种新的强大的数学方法，拉普拉斯-傅立叶变换的有限系统的各种统计模型的精确解析解。其中有一个受约束的版本的统计多重碎裂模型，气体袋模型和丘陵和山谷模型的表面分区。因此，拉普拉斯-傅里叶变换可以使人们在同一个基础上研究核物质状态方程、强子和夸克胶子物质状态方程以及表面配分。对于有限系统，对这些模型的等压分区奇异性进行了完整的分析。发达国家的形式主义，使我们能够，第一次，准确地定义有限体积类似物的气体，液体和混合相的这些模型从统计力学的第一原则，并证明早期的工作的陷阱。所得到的解可用于建立一个新的理论装置来严格研究有限系统中的相变。最后讨论了这些结果所开辟的未来研究的战略方向。
英文摘要：
We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed.
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