利用玻色化推导经典二聚体模型的场论
Derivation of field theory for the classical dimer model using bosonization
AI总结：
本文通过将玻色化应用于Lieb的费米子转移矩阵解，构造性地推导出二维经典二聚体模型的场论，并进一步以微扰和重整化群方法处理含相互作用的双二聚体模型，确定了相边界形状。
摘要：
我们通过对Lieb的（费米子）转移矩阵解应用玻色化，推导出二维经典二聚体模型的场论。我们的构造性方法给出的结果与众所周知的height理论一致，后者此前是基于对称性考虑得到论证的，但我们的方法还确定了有效理论中出现的系数以及微观可观测量与场论中算符之间的对应关系。此外，我们展示了如何以微扰方式在场论中包含相互作用，处理了在两个副本内部及副本之间存在相互作用的双二聚体模型。利用重整化群分析，我们确定了非相互作用点附近相边界的形状，结果与蒙特卡洛模拟一致。
英文摘要：
We derive a field theory for the two-dimensional classical dimer model by applying bosonization to Lieb's (fermionic) transfer-matrix solution. Our constructive approach gives results that are consistent with the well-known height theory, previously justified based on symmetry considerations, but also fixes coefficients appearing in the effective theory and the relationship between microscopic observables and operators in the field theory. In addition, we show how interactions can be included in the field theory perturbatively, treating the case of the double dimer model with interactions within and between the two replicas. Using a renormalization-group analysis, we determine the shape of the phase boundary near the noninteracting point, in agreement with results of Monte Carlo simulations.
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