We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer model with plaquette interaction previously analyzed in previous works. By tuning the edge weights, we can impose a non-zero average tilt for the height function, so that the considered models are in general not symmetric under discrete rotations and reflections. In the determinantal case, height fluctuations in the massless (or ‘liquid’) phase scale to a Gaussian log-correlated field and their amplitude is a universal constant, independent of the tilt. When the perturbation strength $$\lambda $$ λ is sufficiently small we prove, by fermionic constructive Renormalization Group methods, that log-correlations survive, with amplitude A that, generically, depends non-trivially and non-universally on $$\lambda $$ λ and on the tilt. On the other hand, A satisfies a universal scaling relation (‘Haldane’ or ‘Kadanoff’ relation), saying that it equals the anomalous exponent of the dimer–dimer correlation.

中文翻译：

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不可积二聚体：倾斜高度剖面的普遍波动

我们研究了方形晶格上的一类密堆积二聚体模型，存在小而广泛的扰动，使它们成为非决定性的。示例包括接近自由费米子点的 6 顶点模型，以及先前在以前的工作中分析过的具有斑块相互作用的二聚体模型。通过调整边缘权重，我们可以对高度函数施加非零平均倾斜，因此所考虑的模型在离散旋转和反射下通常不对称。在行列式情况下，无质量（或“液体”）相位的高度波动会缩放到高斯对数相关场，并且它们的振幅是一个通用常数，与倾斜无关。当扰动强度 $$\lambda $$ λ 足够小时我们证明，通过费米子构造重整化群方法，对数相关性仍然存在，振幅 A 通常非平凡且非普遍地取决于 $$\lambda $$ λ 和倾斜。另一方面，A 满足通用标度关系（“Haldane”或“Kadanoff”关系），表示它等于二聚体-二聚体相关性的异常指数。