New solutions of the star–triangle relation with discrete and continuous spin variables
New solutions of the star–triangle relation with discrete and continuous spin variables
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DOI：
10.1088/1751-8113/48/43/435201
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发表时间：
2015-04
期刊：
影响因子：
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通讯作者：
A. P. Kels
中科院分区：
文献类型：
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作者：
A. P. Kels
本文对含有整数和真实的分量的相互作用自旋的伊辛型模型，给出了星三角关系的一种新的解法。玻尔兹曼权重的模型中给出的透镜椭圆伽玛函数，并根据山崎最近获得的解决方案的恒星关系。这里给出的星三角关系，意味着Seiberg对偶的4-d = 1？> S 1 × S 3 / Z r？> SU（2）规范理论的指数，以及相应的山崎星-星关系的两分量自旋情形。给出了星三角关系的一个证明，从而得到了一个新的椭圆超几何求和/积分恒等式。本文中的星三角关系包含Bazhanov和Sergeev的主解作为特例。另外两种极限情况下被认为是其中之一，给出了一个新的星三角关系的无限q-产品的比率，而另一种情况下给出了一种新的方式来推导一个星三角关系，是以前得到的作者。
A new solution to the star–triangle relation is given, for an Ising type model of interacting spins containing integer and real valued components. Boltzmann weights of the model are given in terms of the lens elliptic gamma function, and are based on Yamazaki’s recently obtained solution of the star–star relation. The star–triangle relation given here, implies Seiberg duality for the 4−d = 1 ?> S 1 × S 3 / Z r ?> index of the SU(2) quiver gauge theory, and the corresponding two component spin case of the star–star relation of Yamazaki. A proof of the star–triangle relation is given, resulting in a new elliptic hypergeometric summation/integration identity. The star–triangle relation in this paper contains the master solution of Bazhanov and Sergeev as a special case. Two other limiting cases are considered one of which gives a new star–triangle relation in terms of ratios of infinite q-products, while the other case gives a new way of deriving a star–triangle relation that was previously obtained by the author.