Faddeev-Volkov模型的精确解
Exact solution of the Faddeev-Volkov model
摘要：
Faddeev-Volkov模型是一种具有正玻尔兹曼权重的伊辛型晶格模型，其中自旋变量在实数线上取连续值。它作为sinh-Gordon和Liouville模型的晶格模拟，与量子群U_q（sl_2）的模二重化密切相关。在热力学极限下，精确计算了模型的自由能。在准经典极限c->无穷大，模型描述了与黎曼映射定理的瑟斯顿离散模拟相关联的离散共形变换的量子涨落。在强耦合极限c->1时，模型变成了D=2 Zamolodchikov的“渔网”模型的离散版本。
英文摘要：
The Faddeev-Volkov model is an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. It serves as a lattice analog of the sinh-Gordon and Liouville models and intimately connected with the modular double of the quantum group U_q(sl_2). The free energy of the model is exactly calculated in the thermodynamic limit. In the quasi-classical limit c->infinity the model describes quantum fluctuations of discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In the strongly-coupled limit c->1 the model turns into a discrete version of the D=2 Zamolodchikov's ``fishing-net'' model.
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