We propose a generalization of 4-component fermionic model to a two-dimensional hierarchical lattice, in which the unit cell is represented by 4 vertices of a square. In this model the interaction between the spins in the vertices on the diagonal is different from the interaction between the spins in the vertices on the side of the square. We introduce new Gaussian fermionic field which is invariant under the block-spin renormalization group transformation (self-similar field). We describe this field in the Gibbsian form in the finite volume of the hierarchical lattice. We consider the non-Gaussian model in which the Gaussian part is given by the self-similar field and non-Gaussian part is given by the self-interaction. We show that the action of the renormalization group is local and is defined by the finite-dimensional superintegral.

中文翻译：

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分层二维晶格上费米子模型的新变体

我们建议将 4 分量费米子模型推广到二维分层晶格，其中晶胞由正方形的 4 个顶点表示。在这个模型中，对角线上顶点的自旋之间的相互作用不同于正方形边上顶点的自旋之间的相互作用。我们引入了新的高斯费米子场，它在块自旋重整化群变换（自相似场）下是不变的。我们在分层晶格的有限体积中以吉布斯形式描述这个场。我们考虑非高斯模型，其中高斯部分由自相似场给出，非高斯部分由自相互作用给出。我们表明重整化群的作用是局部的，由有限维超积分定义。